Grade 8 Functions: Unit Review

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   A line has a slope of −8 and passes through the point (9, −66). What is its y-intercept?

   1. Write the line as y = mx + b with m = −8.
   2. The point (9, −66) is on the line, so −66 = −8 × 9 + b = −72 + b.
   3. Solve for b: b = −66 − (−72) = 6.
   4. So the y-intercept is 6.

   Answer: 6

2. Example 2

   Function A is y = 5x + 13 and function B is y = 4x + 19. For what value of x do the two functions have the same value of y?

   1. Set the two rules equal: 5x + 13 = 4x + 19.
   2. Subtract 4x from both sides: x + 13 = 19.
   3. Subtract 13 from both sides: x = 19 − 13 = 6.
   4. Check: A gives 5 × 6 + 13 = 43 and B gives 4 × 6 + 19 = 43.
   5. So x = 6.

   Answer: 6

3. Example 3

   Find the slope of the line that passes through (3, 8) and (6, 17).

   1. Slope = change in y ÷ change in x (rise over run).
   2. Change in y: 17 − 8 = 9.
   3. Change in x: 6 − 3 = 3.
   4. Slope = 9 ÷ 3 = 3.
   5. So the slope is 3.

   Answer: 3