Question

determine the equation of the line with the specified slope that passes through the given point. match the correct equation with each given point and slope.
(-3, 4) m = 2
(3, -4) m = 2
(-3, -4) m = 2

y = 2x - 2
y = 2x - 10
y = 2x + 2
y = 2x + 10

Explanation:

Step1: Use point-slope form

The point-slope formula is $y - y_1 = m(x - x_1)$, where $(x_1,y_1)$ is the point and $m$ is the slope.

Step2: Solve for $(-3,4), m=2$

Substitute values: $y - 4 = 2(x - (-3))$
Simplify: $y - 4 = 2x + 6$ → $y = 2x + 10$

Step3: Solve for $(3,-4), m=2$

Substitute values: $y - (-4) = 2(x - 3)$
Simplify: $y + 4 = 2x - 6$ → $y = 2x - 10$

Step4: Solve for $(-3,-4), m=2$

Substitute values: $y - (-4) = 2(x - (-3))$
Simplify: $y + 4 = 2x + 6$ → $y = 2x + 2$

Answer:

$(-3, 4)\ m=2 \longleftrightarrow y=2x+10$
$(3, -4)\ m=2 \longleftrightarrow y=2x-10$
$(-3, -4)\ m=2 \longleftrightarrow y=2x+2$