Question

PLease answer this correctly?

Answer 1

Answer:

$y+4=-\frac{1}{2} (x-5)$

This is the equation of the line perpendicular to the equation line through the points given that crosses through (-4,5)

Step-by-step explanation:

We can write the equation of a line in 3 different forms including slope intercept, point-slope, and standard depending on the information we have. We have a point given and a slope from the equation. We will chose point-slope since we have a point and can find the slope.  

Point slope:$y-y_1=m(x-x_1)$

We must find the slope using the graph. We pick two points which intersect with grid lines from the line given.

Slope:$m=\frac{y_2-y_1}{x_2-x_1}$

We substitute $x_1=3\\y_1=2$ and $x_2=2\\y_2=0$

$m=\frac{0-2}{2-3}$

$m=\frac{-2}{-1}=\frac{2}{1} =2$

$m\neq 2$ in our new equation because it is perpendicular to it. This means we will need to change it into its negative reciprocal which is $m=-\frac{1}{2}$.

We will substitute $m=-\frac{1}{2}$ and now use the point they gave us (-4,5) $x_1=-4\\y_1=5$.

$y-(-4)=-\frac{1}{2} (x-5)$

$y+4=-\frac{1}{2} (x-5)$

This is the equation of the line perpendicular to the equation line through the points given that crosses through (-4,5)