Question

albert drew the line represented by this equation on a coordinate plane.
$y = \frac{1}{2}x + 5$
on the same coordinate plane, penny drew a line that is perpendicular to albert’s line and passes through the point(-4,
which of the following equations represents penny’s line?
\\(\circ\\) $y = 2x + 5$
\\(\circ\\) $y = -2x - 15$
\\(\circ\\) $y = 2x + 11$
\\(\circ\\) $y = -2x - 11$

Explanation:

Step1: Find perpendicular slope

The slope of Albert's line is $\frac{1}{2}$. Perpendicular slopes multiply to $-1$, so:
$$m \times \frac{1}{2} = -1 \implies m = -2$$

Step2: Use point-slope form

Use point $(-4, -3)$ and $m=-2$ in $y - y_1 = m(x - x_1)$:
$$y - (-3) = -2(x - (-4))$$

Step3: Simplify to slope-intercept form

Expand and isolate $y$:
$$y + 3 = -2x - 8 \implies y = -2x - 11$$

Answer:

y = -2x - 11