Question

How do I do this, please explain​

Answer 1

1.
`y=(1)/(3)x+14`

2.
`y=1.25x+27`

Explanation:

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

`(x-x_1)/(x_2-x_1)=(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

`(x-(-18))/(-9-(-18))=(y-8)/(11-8)\\ \\(x+18)/(-9+18)=(y-8)/(3)\\ \\(x+18)/(9)=(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=(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)=(-1)/(-0.8)=(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`