How to plot a linear equation graph - BBC Bitesize (2024)

Key points

How to plot a linear equation graph - BBC Bitesize (1)

  • Graphs of two or more straight lines can be used to solve simultaneous linear equations.

  • The graph of a straight line can be described using an .

    • lines are written as \(y = c\)
    • lines are written as \(x = c\)
    • are written as \(y = mx + c\)
  • \(m\) is a number which is a measure of the steepness of the line. This is the .

  • \(c\) is the number where the line crosses the \(y\)-axis. This is the \(y\).

  • The of the points on an oblique line are calculated by given values of \(x\) into the equation \(y = mx + c\)

How to plot a linear equation graph - BBC Bitesize (2)

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Recognise and draw the lines π’š = 𝒙 and π’š = -𝒙

All the points on the line \(y = x\) have coordinates with equal values for \(x\) and \(y\)

  • To draw the line \(y = x\):
    1. Plot points with coordinates where \(x\) and \(y\) are equal. Three points are sufficient, but more can be plotted.
    2. Draw a line through the plotted points.

All the points on the line \(y = -x\) have coordinates with values for \(x\) and \(y\) that are equal in but with opposite signs.

If \(x\) is positive, \(y\) is negative. If \(x\) is negative, \(y\) is positive.

  • To draw the line \(y = -x\):
    1. Plot points with coordinates where \(x\) and \(y\) have equal magnitude but opposite signs.
    2. Draw a line through the plotted points.

Examples

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  1. How to plot a linear equation graph - BBC Bitesize (3)

Slide 1 of 6, Label to the left of a graph y equals x. Graph showing the x axis and y axis increasing in units of five and ten and decreasing in units of minus five and minus ten. Intersecting diagonally through the origin point labelled, open brackets, nought, nought close brackets and below is the word origin. The positive plot line rises to the right through two points. The first point is open bracket four, four close bracket. The second point is open bracket six, six close bracket. At the top end of the plot line is y equals x. At the origin point, the plot line representing negative descends diagonally to the left with two points labelled open bracket minus four, minus four, close bracket and open bracket, minus eight, minus eight, close bracket., The straight line π’š = 𝒙 passes through the origin. All the points on the line π’š = 𝒙 have coordinates with equal values for 𝒙 and π’š

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Question

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Draw the graph π’š = π’Žπ’™ + 𝒄 by creating a table of values

\(m\) is a number which measures the steepness of the line. This is known as the gradient.

\(c\) is the number where the line crosses the \(y\)-axis. This is the \(y\)-intercept.

  • To draw a graph of \(y = mx + c\) for given values of \(x\):
    1. Use the given values for \(x\) to draw a table of values for \(x\) and \(y\)
    2. each value of \(x\) into the equation to find the valueof \(y\). Each pair of values give a coordinate.
    3. Use the coordinates to decide on that will take all the values of \(x\) and \(y\)
    4. Plot the coordinates and draw a line through the points. Label the line with the equation.

Example

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  1. How to plot a linear equation graph - BBC Bitesize (5)

Slide 1 of 9, Y equals two x minus five. Minus one is less than or equal to x, which is less than or equal to three., Draw the graph of π’š = 2𝒙 – 5 for values of 𝒙 from -1 to 3. This is written as the inequality -1 ≀ 𝒙 ≀ 3

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Questions

Question 1: Complete the table of values for \(y = 3x + 8\) for values of \(x\) from -2 to 2

How to plot a linear equation graph - BBC Bitesize (6)

A table of values can also be used to find the coordinates of a line with a negative gradient.

Question 2: Complete the table of values for \(y = 3 – 2x\) for values of \(x\) from -1 to 3

How to plot a linear equation graph - BBC Bitesize (7)

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Reading 𝒙 and π’š coordinates from a graph

A position on a graph is defined by coordinates (\(x\), \(y\)). When one coordinate is given, the second can be read from the graph.

  • To find a \(y\)-coordinate from a given \(x\)-coordinate:

    1. On the \(x\)-axis, locate the given amount.
    2. Draw a vertical line, using a ruler, from the given amount up to the line.
    3. Draw a horizontal line, using a ruler, from the line across to the \(y\)-axis.
    4. Read the value on the \(y\)-axis.
  • To find an \(x\)-coordinate from a given \(y\)-coordinate:

    1. On the \(y\)-axis, locate the given amount.
    2. Draw a horizontal line, using a ruler, from the given amount across to the line.
    3. Draw a vertical line, using a ruler, from the line down to the \(x\)-axis.
    4. Read the value on the \(x\)-axis.

Examples

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  1. How to plot a linear equation graph - BBC Bitesize (8)

Slide 1 of 6, Example one. A graph showing the x axis increasing from minus five to five and the y axis increasing in units of tens from minus ten to thirty, they intersect at zero comma zero. An oblique line slopes up the graph from left to right labelled y equals five x plus four. To the right of the graph, the equations x equals four and y equals question mark., Use the graph to find the value of π’š when 𝒙 = 4

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Question

Use the graph to find the value of \(x\) when \(y = 3\)

How to plot a linear equation graph - BBC Bitesize (9)

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Practise reading and plotting linear equation graphs

Quiz

Practise reading and plotting linear equation graphs with this quiz. You may need a pen and paper to help you.

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Real-life maths

How to plot a linear equation graph - BBC Bitesize (10)

Linear graphs are commonly used when converting between different units of measurement.

For example, swapping between temperatures in degrees Celsius (Β°C) and degrees Fahrenheit (Β°F), exchanging between different currencies, such as pounds and euros, or changing inches into centimetres.

How to plot a linear equation graph - BBC Bitesize (11)

How to plot a linear equation graph - BBC Bitesize (12)

Linear graphs are useful to pharmacists and scientists in the pharmaceutical industry when working out the correct strength of drugs.

The amount of a drug for a given volume of medicine is critical, both for the medicine to be effective and for the safety of the patient.

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Game - Divided Islands

Play the Divided Islands game! gamePlay the Divided Islands game!

Using your maths skills, help to build bridges and bring light back to the islands in this free game from BBC Bitesize.

How to plot a linear equation graph - BBC Bitesize (13)

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How to plot a linear equation graph - BBC Bitesize (2024)

FAQs

How to plot a linear equation graph - BBC Bitesize? β€Ί

1) Choose three values for x. Substitute these values in the equation and solve to find the corresponding y-coordinates. 2) Plot the ordered pairs found in step 1. 3) Draw a straight line through the plotted points.

How to plot a graph of a linear equation? β€Ί

1) Choose three values for x. Substitute these values in the equation and solve to find the corresponding y-coordinates. 2) Plot the ordered pairs found in step 1. 3) Draw a straight line through the plotted points.

How do you graph linear functions step by step? β€Ί

  1. Choose a minimum of two input values.
  2. Evaluate the function at each input value.
  3. Use the resulting output values to identify coordinate pairs.
  4. Plot the coordinate pairs on a grid.
  5. Draw a line through the points.
Feb 9, 2020

How to do linear equations step by step? β€Ί

The steps for solving linear equations are:
  1. Simplify both sides of the equation and combine all same-side like terms.
  2. Combine opposite-side like terms to obtain the variable term on one side of the equal sign and the constant term on the other.
  3. Divide or multiply as needed to isolate the variable.
  4. Check the answer.
Oct 6, 2021

What does a linear graph look like? β€Ί

Linear graph is represented in the form of a straight line. To show a relationship between two or more quantities we use a graphical form of representation. If the graph of any relation gives a single straight line then it is known as a linear graph. The word "linear" stands for a straight line.

How do you plot a graph step by step? β€Ί

  1. Step 1: Identify the variables. ...
  2. Step 2: Determine the variable range. ...
  3. Step 3: Determine the scale of the graph. ...
  4. Step 4: Number and label each axis and title the graph.
  5. Step 5: Determine the data points and plot on the graph. ...
  6. Step 6: Draw the graph.

What are three methods used to graph a linear equation? β€Ί

There are three basic methods of graphing linear functions. The first is by plotting points and then drawing a line through the points. The second is by using the y-intercept and slope. The third is applying transformations to the identity function f(x)=x f ( x ) = x .

What is the formula for a linear graph? β€Ί

Given the graph of a line, you can determine the equation in two ways, using slope-intercept form, y=mx+b, or point-slope form, yβˆ’y1=m(xβˆ’x1). The slope and one point on the line is all that is needed to write the equation of a line. All nonvertical lines are completely determined by their y-intercept and slope.

How to draw a linear graph? β€Ί

Steps for Plotting Linear Graph
  1. Step 1: Convert the equation in the form y = mx + c. ...
  2. Step 2: Now we have to replace the value of x and find the subsequent values of y in order to create the coordinates.
  3. Step 3: Starting with putting x = 0 in the above equation, we get y = -4.
May 3, 2023

How to draw the graph of a linear equation and plane? β€Ί

Graphing of Linear Equations keypoints

Therefore, every linear equation in two variables can be represented geometrically as a straight line in a coordinate plane. Points on the line are the solution of the equation. This why equations with degree one are called as linear equations.

What is the point plotting method? β€Ί

Using point plotting, one associates an ordered pair of real numbers (x, y) with a point in the plane in a one-to-one manner. As a result, one obtains the 2-dimensional Cartesian coordinate system.

How do you plot a system of linear equations on a graph? β€Ί

Graphing a system of linear equations is as simple as graphing two straight lines. When the lines are graphed, the solution will be the (x,y) ordered pair where the two lines intersect (cross). * Before you begin, rearrange the equations so they will read "y =".

How do you write a linear equation from a chart? β€Ί

Given the graph of a line, you can determine the equation in two ways, using slope-intercept form, y=mx+b, or point-slope form, yβˆ’y1=m(xβˆ’x1). The slope and one point on the line is all that is needed to write the equation of a line. All nonvertical lines are completely determined by their y-intercept and slope.

How to plot points on a linear graph? β€Ί

To graph a linear equation by plotting points, you can use the intercepts as two of your three points. Find the two intercepts, and then a third point to ensure accuracy, and draw the line. This method is often the quickest way to graph a line.

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