The y-intercept is where the line starts
For y = 2x + 1, the line crosses the y-axis at 1.
rise 2 for each 1 across
starts at y = 1
Read c first, then use the gradient to move from point to point.
Year 8
Plot and interpret linear graphs from y = mx + c
Plot points from y = mx + c, interpret gradient and y-intercept, and explain why parallel lines have the same gradient.
Lesson overview
Algebra - straight-line graphs
A straight-line graph can be written in the form y = mx + c. The number c tells us where the line crosses the y-axis. The number m tells us the gradient, which is how much y changes when x increases by 1. To plot the graph, calculate some pairs of x and y values, mark the points, and join them with a straight line.
Tables help you plot accurately
For y = x + 3, substitute x values to build the line.
| x | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| y | 3 | 4 | 5 | 6 |
Each x value gives one coordinate pair on the line.
Parallel lines share the same gradient
These two lines rise by 1 each time x increases by 1, so they are parallel.
y = x + 1y = x + 4
Different intercepts can shift the line up or down, but equal gradients keep the lines parallel.
Worked example
Plot y = 2x + 1 for x = 0, 1, 2 and 3.
| x | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| y | 1 | 3 | 5 | 7 |
- Start with the rule y = 2x + 1.
- Substitute x = 0, 1, 2 and 3 to get y values of 1, 3, 5 and 7.
- Plot the points (0,1), (1,3), (2,5) and (3,7).
- Join the points with a straight line because the relationship is linear.
Try it
Use the equation to build coordinate pairs, then think about what the gradient and intercept are telling you.
Question 1
For y = 2x + 1, what is y when x = 3?
Question 2
Which point lies on the line y = x + 4?
| x | 2 |
|---|---|
| y | 6 |
Question 3
What is the y-intercept of y = 3x + 2?
Question 4
Which line is parallel to y = 2x + 1?
Question 5
A taxi fare is modeled by y = 3x + 4, where x is miles and y is pounds. What does the 4 mean?
Common mistakes
Watch for these when working through the lesson.
- Mixing up the gradient and the y-intercept.
- Substituting x values incorrectly when building the table.
- Assuming lines are parallel just because they both rise.
Related topics
These ideas fit closely with this lesson.
- Solve two-step linear equations.
- Simplify expressions review.
- Expand single brackets.