Question

the slope - intercept form of the equation of a line that passes through point (-2, -13) is y = 5x - 3. what is the point - slope form of the equation for this line?
○ y - 13 = 5(x - 2)
○ y + 13 = 5(x + 2)
○ y - 2 = 5(x - 13)
○ y + 2 = 5(x + 13)

Explanation:

Step1: Recall point-slope formula

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

Step2: Identify values from given info

From $y=5x-3$, slope $m=5$. The point is $(-2, -13)$, so $x_1=-2$, $y_1=-13$.

Step3: Substitute into the formula

Substitute values: $y - (-13) = 5(x - (-2))$
Simplify signs: $y + 13 = 5(x + 2)$

Answer:

C. $y + 13 = 5(x + 2)$