Graphs
Grade 4-6Straight Line Graphs
Every straight line graph follows the same rule, y = mx + c, and once you can read the gradient and intercept from that equation, questions about tables of values, crossing points and checking coordinates all use the same idea. This lesson covers reading the gradient and y-intercept, substituting values of x to find y, finding the equation of a line from its graph, and finding where a line crosses the axes.
What you need to know
- Every straight line can be written y = mx + c, where m is the gradient and c is the y-intercept.
- c is where the line crosses the y-axis; m tells you how steep it is.
- To plot one, make a short table of x and y values, or use the gradient and intercept.
- Rearrange into y = mx + c form before reading off the gradient.
Written by Asad, co-founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Reading the gradient and y-intercept from y = mx + c
In the equation y = mx + c, m is the gradient, which tells you how steep the line is and whether it slopes up or down, and c is the y-intercept, the value of y where the line crosses the y-axis.
For y = 3x + 5, the gradient is 3 and the y-intercept is 5. For y = -2x + 7, the gradient is -2, showing the line slopes downward, and the y-intercept is 7.
Substituting values of x to find y
To find the value of y for a given value of x, substitute that value into the equation and work through the arithmetic carefully, especially when x is negative.
For y = 2x + 1, when x = -1: y = 2 × -1 + 1 = -1. When x = 3: y = 2 × 3 + 1 = 7.
Finding the equation of a line from its graph
Read the y-intercept directly from where the line crosses the y-axis. Find the gradient by picking two points on the line and working out how much y increases for every one unit x increases.
A line crossing the y-axis at 2, and rising 1 unit for every 1 unit moved to the right, has gradient 1 and y-intercept 2, giving the equation y = x + 2.
Finding where a line crosses the axes, and checking a point
A line crosses the y-axis where x = 0, and crosses the x-axis where y = 0. Substitute the relevant value and solve for the other coordinate. To check whether a point lies on a line, substitute the x-coordinate into the equation and see whether the result matches the given y-coordinate.
For y = 2x - 6: the y-axis crossing is at x = 0, giving y = -6, so (0, -6). The x-axis crossing is at y = 0, giving 0 = 2x - 6, so x = 3, giving (3, 0).
Worked examples
Three exam-style questions, fully solved
For the line y = 3x + 5, write down the gradient and the y-intercept.
Easy- 1.Compare the equation to y = mx + c
- 2.The number in front of x is the gradient: 3
- 3.The number added on its own is the y-intercept: 5
Answer: Gradient 3, y-intercept 5
Find the coordinates of the points where the line y = 2x - 6 crosses the x-axis and the y-axis.
Medium- 1.For the y-axis, substitute x = 0: y = 2 × 0 - 6 = -6, giving (0, -6)
- 2.For the x-axis, substitute y = 0: 0 = 2x - 6
- 3.Solve for x: 2x = 6, so x = 3, giving (3, 0)
Answer: (0, -6) and (3, 0)
Does the point (3, 7) lie on the line y = 2x + 1? Show how you know.
Hard- 1.Substitute the x-coordinate into the equation: y = 2 × 3 + 1
- 2.Work out the result: y = 7
- 3.Compare this to the given y-coordinate: 7 matches 7
Answer: Yes, since 2 × 3 + 1 = 7, which matches the y-coordinate
Practice
6 questions, marked instantly
Type an answer and check it. The worked solution appears once you have had a go. No login needed, and your progress saves in this browser.
Practice
Now try these yourself.
Type your answer and check it. The worked solution appears once you have had a go.
What is the gradient of the line y = 3x − 5?
Where does the line y = 2x + 7 cross the y-axis? Give the y-coordinate.
A line has a gradient of 4 and passes through (0, −1). Write its equation.
Does the point (3, 8) lie on the line y = 2x + 2? Answer yes or no.
Rearrange 2y = 6x + 4 into the form y = mx + c. Write the full equation.
What is the gradient of the line y = 7 − 2x?
Avoid these
The mistakes students make most often
Mixing up the gradient and y-intercept when reading y = mx + c, for example giving the y-intercept as the gradient.
Losing a negative sign when substituting a negative value of x into the equation.
Confusing where a line crosses the x-axis with where it crosses the y-axis, and setting the wrong variable to zero.
When checking whether a point lies on a line, substituting the y-coordinate into the equation instead of the x-coordinate.
When reading the gradient from a graph, miscounting the number of squares moved up or across between two points on the line.
FAQ
Questions students and parents ask
Before this topic, make sure you know
What to learn next
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