what is the equation of the line that is perpendicular to the given line and has an x - intercept of 6?\n$y…

Explanation:

Step1: Find slope of given line

The slope $m$ of a line passing through two points $(x_1,y_1)=(-4,4)$ and $(x_2,y_2)=(4, - 2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-2 - 4}{4+4}=\frac{-6}{8}=-\frac{3}{4}$.

Step2: Find slope of perpendicular line

If two lines are perpendicular, the product of their slopes is - 1. Let the slope of the perpendicular line be $m_1$. Then $m\times m_1=-1$. Since $m =-\frac{3}{4}$, we have $-\frac{3}{4}m_1=-1$, so $m_1=\frac{4}{3}$.

Step3: Use x - intercept to find y - intercept

The x - intercept is 6, so the line passes through the point $(6,0)$. The equation of a line is $y = m_1x + b$, substituting $x = 6$, $y = 0$ and $m_1=\frac{4}{3}$ into it: $0=\frac{4}{3}\times6 + b$. Simplify the right - hand side: $\frac{4}{3}\times6=8$, so $0 = 8 + b$, and $b=-8$. The equation of the line is $y=\frac{4}{3}x - 8$.

Answer:

C. $y=\frac{4}{3}x - 8$