Grade 8 Functions: Linear Functions

Worked examples

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

1. Example 1

   For the linear function y = 4x − 7, what value of x makes y = 1?

   1. Set the rule equal to 1: 4x − 7 = 1.
   2. Undo the − 7: 4x = 1 + 7 = 8.
   3. Divide both sides by 4: x = 8 ÷ 4 = 2.
   4. Check: 4 × 2 − 7 = 1.
   5. So x = 2.

   Answer: 2

2. Example 2

   The graph of y = −8x − 3 is a straight line. It passes through the point (2, ?). What is the missing y-coordinate?

   1. Every point (x, y) on the graph makes the rule true, so put the x-coordinate into the rule.
   2. Substitute x = 2: y = −8 × 2 − 3 = −16 − 3 = −19.
   3. So the point is (2, −19), and the missing y-coordinate is −19.

   Answer: −19

3. Example 3

   Data: x (x) and y (y)

   x	1	2	3	4
   y	5	7	9	11

   The graph shows a linear function. Its line passes through the marked points. Where does the line cross the y-axis? What is the y-intercept of the line?

   1. Read two marked points off the graph (or its table): (1, 5) and (2, 7).
   2. Slope = change in y ÷ change in x (rise over run), using the two points on the line.
   3. Change in y: 7 − 5 = 2. Change in x: 2 − 1 = 1.
   4. Slope = 2 ÷ 1 = 2.
   5. The y-intercept is the value of y at x = 0, where the drawn line crosses the y-axis. Check it with the slope. Use b = y − m·x with the point (1, 5): b = 5 − 2 × 1 = 5 − 2 = 3.
   6. So the y-intercept is 3.

   Answer: 3