Question

a line passes through the point (-2,-3) and is perpendicular to the line y=1/2x - 1. what is its equation?
○ y=-2x - 3
○ y=1/2x - 3
○ y=-2x - 7
○ y=1/2x - 7

Explanation:

Step1: Find perpendicular slope

The slope of $y=\frac{1}{2}x-1$ is $\frac{1}{2}$. Perpendicular slopes are negative reciprocals, so $m = -2$.

Step2: Substitute point into slope-intercept form

Use point $(-2,-3)$ and $y=mx+b$:
$$-3 = -2(-2) + b$$

Step3: Solve for y-intercept b

$$-3 = 4 + b$$
$$b = -3 - 4 = -7$$

Step4: Write final line equation

Substitute $m=-2$ and $b=-7$ into $y=mx+b$.

Answer:

y=-2x-7 (Option C)