Question

a line has a slope of -3. which of the following points also lies on the line if it passes through (1,5)?
(3,5)
(2,8)
(0,2)
(2,2)

Explanation:

Step1: Find line equation (point-slope)

Use point-slope form $y - y_1 = m(x - x_1)$, where $m=-3$, $x_1=1$, $y_1=5$.
$y - 5 = -3(x - 1)$

Step2: Simplify to slope-intercept form

Expand and rearrange to solve for $y$.
$y = -3x + 3 + 5$
$y = -3x + 8$

Step3: Test each point

Substitute each option into $y=-3x+8$:

• For (3,5): $y=-3(3)+8=-1

eq 5$

• For (2,8): $y=-3(2)+8=2

eq 8$

• For (0,2): $y=-3(0)+8=8

eq 2$

• For (2,2): $y=-3(2)+8=2$, which matches.

Answer:

(2,2)