Question

A line has a slope of -2 and a y-intercept of –3. Graph the line using the slope and y-intercept.

Which of the following points lie on this same line?
(–2, 0)
(–1.5, 0)
(–6, 9)
(2, –3)
(3, –9)
(–4, 4)

Answer 1

The line is y = −2x − 3. To graph: plot the y-intercept (0, −3) and use the slope −2 (down 2 for each 1 to the right, or up 2 for each 1 to the left).

Check each point by substituting x into y = −2x − 3:

- (−2, 0): y = −2(−2) − 3 = 4 − 3 = 1 → no
- (−1.5, 0): y = −2(−1.5) − 3 = 3 − 3 = 0 → yes
- (−6, 9): y = −2(−6) − 3 = 12 − 3 = 9 → yes
- (2, −3): y = −2(2) − 3 = −4 − 3 = −7 → no
- (3, −9): y = −2(3) − 3 = −6 − 3 = −9 → yes
- (−4, 4): y = −2(−4) − 3 = 8 − 3 = 5 → no

Points on the line: (−1.5, 0), (−6, 9), (3, −9).