Answer:
1. [tex]y=\dfrac{1}{3}x+14[/tex]
2. [tex]y=1.25x+27[/tex]
Step-by-step explanation:
1. The equation of the line passing through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is
[tex]\dfrac{x-x_1}{x_2-x_1}=\dfrac{y-y_1}{y_2-y_1}[/tex]
In your case, the line passes through the points (-18,8) and (-9,11). So, its equation is
[tex]\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[/tex]
In the slope intercept form this equation is
[tex]3y=x+42\\ \\y=\dfrac{1}{3}x+14[/tex]
2. First, find the slope of the line [tex]4x+5y=1,012:[/tex]
[tex]5y=1,012-4x\\ \\y=202.4-0.8x[/tex]
Thus, the slope of this line is [tex]m=-0.8[/tex]
Two perpendicular line have the slopes with their product equal to -1:
[tex]m_{\perp}\cdot m=-1\\ \\m_{\perp}=\dfrac{-1}{-0.8}=\dfrac{10}{8}=1.25[/tex]
The equation of perpendicular line is
[tex]y-y_1=m_{\perp}(x-x_1),[/tex]
where [tex](x_1,y_1)[/tex] are the coordinates of the point the line passes through. So,
[tex]y-22=1.25(x-(-4))\\ \\y-22=1,25(x+4)\\ \\y=22+1.25x+5\\ \\y=1.25x+27[/tex]
