Linear graphs

A linear equation in the form y = mx + c graphs as a straight line, where m is the gradient (how steep the line is — rise over run) and c is the y-intercept (where the line crosses the y-axis). A positive gradient slopes upward left to right; a negative gradient slopes downward. To graph a line, plot the y-intercept first, then use the gradient to find a second point.

Key terms

Gradient:

The steepness of a line, calculated as rise over run.

Y-intercept:

The point where a line crosses the y-axis.

Questions

1. 1. In y = mx + c, m represents the:

   • Gradient
   • Y-intercept
   • X-value
   • A constant with no meaning

2. 2. In y = mx + c, c represents the:

   • Gradient
   • Y-intercept
   • Gradient squared
   • Nothing important

3. 3. For y = 3x + 2, what is the y-intercept?

   • 3
   • 2
   • 5
   • 0

4. 4. For y = 3x + 2, what is the gradient?

   • 3
   • 2
   • 5
   • 0

5. 5. A positive gradient means the line slopes:

   • Upward, left to right
   • Downward, left to right
   • Perfectly flat
   • Vertically only

6. 6. A negative gradient means the line slopes:

   • Upward, left to right
   • Downward, left to right
   • Perfectly flat
   • Vertically only

7. 7. The y-intercept is the point where a line crosses the:

   • Y-axis
   • X-axis
   • Origin only
   • Nothing, it never crosses anything

8. 8. For y = −2x + 5, what is the gradient?

   • −2
   • 5
   • 2
   • −5

9. 9. For y = −2x + 5, what is the y-intercept?

   • −2
   • 5
   • 2
   • −5

10. 10. A line with gradient 0 is:

    • Perfectly horizontal
    • Perfectly vertical
    • Impossible to draw
    • Always negative

11. 11. A line passes through (0, 4) and has gradient 2. What is its equation?

    • y = 2x + 4
    • y = 4x + 2
    • y = 2x − 4
    • y = 4x − 2

12. 12. Gradient is calculated as:

    • Rise over run
    • Run over rise
    • Rise plus run
    • Rise minus run

13. 13. A line goes up 4 units for every 2 units it goes right. What is its gradient?

    • 1
    • 2
    • 4
    • 6

14. 14. For the equation y = x − 3, what is the y-intercept?

    • 1
    • −3
    • 3
    • 0

15. 15. A phone plan costs $20 upfront plus $5 per GB used (y = 5x + 20). What does the y-intercept represent?

    • The fixed upfront cost with 0 GB used
    • The cost per gigabyte
    • The total number of gigabytes
    • Nothing meaningful

16. 16. Using y = 5x + 20 (a phone plan), what does the gradient of 5 represent?

    • The cost per gigabyte used
    • The fixed upfront fee
    • The total bill
    • The number of days in the plan

17. 17. Two lines both have gradient 3 but different y-intercepts. These lines are:

    • Parallel, never meeting
    • Identical in every way
    • Perpendicular
    • Impossible to graph

18. 18. A line passes through (0, −2) and (2, 4). What is its gradient?

    • 2
    • 3
    • 4
    • 6

19. 19. For a line with equation y = −3x + 1, as x increases, y:

    • Decreases
    • Increases
    • Stays exactly the same
    • Becomes undefined

20. 20. A steeper line (compared to a flatter one) has a gradient that is:

    • Larger in absolute value
    • Always exactly 0
    • Always negative
    • Always equal to the y-intercept

21. 21. A savings account starts with $50 and grows by $10 a week (y = 10x + 50). After how many weeks will it reach $150?

    • 5
    • 10
    • 15
    • 20