Question

question 8 of 10, step 1 of 1 find the equation of the line which passes through the point (-1, -4), and is perpendicular to the line with the equation y = -2x + 6. express your answer in slope-intercept form. simplify your answer.

Explanation:

Step1: Identify perpendicular slope

The slope of $y=-2x+6$ is $-2$. The slope of a perpendicular line is the negative reciprocal: $m=\frac{1}{2}$.

Step2: Use point-slope form

Point-slope formula: $y-y_1=m(x-x_1)$. Substitute $m=\frac{1}{2}$, $x_1=-1$, $y_1=-4$:
$y-(-4)=\frac{1}{2}(x-(-1))$

Step3: Simplify to slope-intercept form

Simplify and solve for $y$:
$y+4=\frac{1}{2}(x+1)$
$y+4=\frac{1}{2}x+\frac{1}{2}$
$y=\frac{1}{2}x+\frac{1}{2}-4$
$y=\frac{1}{2}x-\frac{7}{2}$

Answer:

$y=\frac{1}{2}x-\frac{7}{2}$