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Straight Line Graph Equation

An online exercise about the equation y=mx+c and the features of a straight line graph.
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This is level 1: The equation of a straight line. You will be awarded a trophy if you get at least 7 answers correct and you do this activity online.

1

What is the gradient of the line described by the equation \(y=4x-2\) ?

The gradient is the coefficient (number in front) of \(x\)

☐ ☐ ✓ ✗

2

What is the y-intercept of the line \(y=9x+3\) ?

The y-intercept is the number written on its own, not multiplied by \(x\).

☐ ☐ ✓ ✗

3

What is the gradient of the line described by the equation \(2y-8x=2\) ?

First rearrange the equation of the line into the form \(y=mx+c\).
Then the gradient is the coefficient of \(x\)

☐ ☐ ✓ ✗

4

What is the y-intercept of the line \(3y+4x-27=0\)?

First rearrange the equation of the line into the form \(y=mx+c\).
Then the y-intercept is the number written on its own, not multiplied by \(x\).

☐ ☐ ✓ ✗

5

Which of the following points are on the line \(y=8x-6\) ?

      A(1,2), B(2,11), C(3,18), D(4,25), E(5,34), F(6,27), G(7,50).

      Rearrange the letters of your answer to make a dictionary word.

For each point, test the values of \(x\) and \(y\) to see if they satisfy the equation \(y=8x-6\).

☐ ☐ ✓ ✗

6

The point (3, t) lies on the line \(y=2x-8\). Find the value of \(t\).

☐ ☐ ✓ ✗

7

The point (s, 3) lies on the line \(3y-2x=8\). Find the value of \(s\).

☐ ☐ ✓ ✗

8

Find the equation of the line that has a gradient of 2 and passes through the point (2,15). Give your answer in the form \(y=mx+c\)

☐ ☐ ✓ ✗

9

Find the equation of the line that passes through P(-5,-1) and R(8,-14)?
Give your answer in the form \(y=mx+c\)

☐ ☐ ✓ ✗

10

A straight line passes through P(2,8) and R(-6,-8)?
Find the equation of the line in the form \(ay+bx+c=0\).

☐ ☐ ✓ ✗

Check

Can you correct your mistakes in order to get full marks?

This is Straight Line Graph Equation level 1. You can also try:
Gradient Graph Match Level 2

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.
Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 1 February 'Starter of the Day' page by M Chant, Chase Lane School Harwich:

"My year five children look forward to their daily challenge and enjoy the problems as much as I do. A great resource - thanks a million."

Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay:

"An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!"

Whose Idea Was This?

Did you enjoy doing this 'Straight Line Graph Equation' activity? Are you curious about who originally came up with this idea in Maths? Discover more about one of the mathematicians who is associated with this concept.
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Description of Levels

Plot - Complete a table of values then plot the corresponding points to create a graph.

Match - Match the graphs with their equations or descriptions in this interactive drag-and-drop activity.

V & H - Questions about the equations of straight line graphs that are parallel to the axes.

Level 1 - The equation of a straight line

Level 2 - Parallel and perpendicular lines

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More Graphs Activities including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Example

In general, the equation of a straight line can be written in the form \(y = mx + c\).

In this equation, \(m\) represents the gradient of the line. The gradient describes how steep the line is and can be calculated as the change in \(y\) divided by the change in \(x\). This is often described as the rise over the run.

The letter \(c\) represents the \(y\)-intercept of the line. This is the point where the line crosses the \(y\)-axis.

A horizontal line has gradient zero, so its equation is of the form \(y = c\), where \(c\) is a constant.

A vertical line cannot be written in the form \(y = mx + c\). Its equation is of the form \(x = d\), where \(d\) is a constant. This line crosses the \(x\)-axis at \((d, 0)\).

If two lines are parallel, they have the same gradient.

If two lines are perpendicular, the gradient of one line is the negative reciprocal of the gradient of the other. For example, if one line has gradient \(2\), a line perpendicular to it will have gradient \(-\frac{1}{2}\).

Some questions have a hint that can help you find a way to solve the problem. If you see a  button, click it to reveal the hint.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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