Question

PLSSSSS HELP!!!!!

Answer 1

Answer:

$\displaystyle y - 8 = -\frac{2}{5}\, (x + 7)$ is perpendicular to $\displaystyle y - 4 = \frac{5}{2} \, (x + 3)$ and goes through the point $(-7,\, 8)$.

Step-by-step explanation:

Consider a line that has a slope of $m$ and goes through the point $(x_{0},\, y_{0})$. The point-slope equation of this line would be:

$y - y_{0} = m\, (x - x_{0})$.

The equation of "the given line" in this question is in the point-slope form. Compare the equation of this given line to $y - y_{0} = m\, (x - x_{0})$. $m = (5/2)$.

The coefficient of $x$ would be $m = (5 / 2)$. In other words, the slope of this given line would be $(5/2)$.

If two lines are perpendicular to one another, the product of their slopes would be $(-1)$.

Since the slope of the given line is $(5 / 2)$, the slope of a line perpendicular to this line would be:

$\displaystyle \frac{-1}{5 / 2} = -\frac{2}{5}$.

The question requested that this line should go through the point $(-7,\, 8)$. Since the slope of that line is found to be $(-2/5)$, the point-slope equation of that line would be:

$\displaystyle y - 8 = -\frac{2}{5}\, (x - (-7))$.

Simplify this equation to get:

$\displaystyle y - 8 = -\frac{2}{5}\, (x + 7)$.