Question

How do I do this, please explain​

Answer 1

Answer:

1. $y=\dfrac{1}{3}x+14$

2. $y=1.25x+27$

Step-by-step explanation:

1. The equation of the line passing through the points $(x_1,y_1)$ and $(x_2,y_2)$ is

$\dfrac{x-x_1}{x_2-x_1}=\dfrac{y-y_1}{y_2-y_1}$

In your case, the line passes through the points (-18,8) and (-9,11). So, its equation is

$\dfrac{x-(-18)}{-9-(-18)}=\dfrac{y-8}{11-8}\\ \\\dfrac{x+18}{-9+18}=\dfrac{y-8}{3}\\ \\\dfrac{x+18}{9}=\dfrac{y-8}{3}\\ \\3(x+18)=9(y-8)\\ \x+18=3(y-8)\\ \\x+18=3y-24\\ \\x-3y+18+24=0\\ \\x-3y+42=0$

In the slope intercept form this equation is

$3y=x+42\\ \\y=\dfrac{1}{3}x+14$

2. First, find the slope of the line $4x+5y=1,012:$

$5y=1,012-4x\\ \\y=202.4-0.8x$

Thus, the slope of this line is $m=-0.8$

Two perpendicular line have the slopes with their product equal to -1:

$m_{\perp}\cdot m=-1\\ \\m_{\perp}=\dfrac{-1}{-0.8}=\dfrac{10}{8}=1.25$

The equation of perpendicular line is

$y-y_1=m_{\perp}(x-x_1),$

where $(x_1,y_1)$ are the coordinates of the point the line passes through. So,

$y-22=1.25(x-(-4))\\ \\y-22=1,25(x+4)\\ \\y=22+1.25x+5\\ \\y=1.25x+27$