14.
First, we need to find the slope m of the given line. A parallel line to the given one will have that same slope m.
And a perpendicular line will have a slope that is the negative reciprocal of m.
Since the given line passes through points (-3, 3) and (-2, -1), its slope m is given :
[tex]m=\frac{-1-3_{}}{-2-(-3)}=\frac{-4}{-2+3}=\frac{-4}{1}=-4[/tex]
a). Now, a parallel line also has slope -4. And since it needs to pass through the point (-4, 0), we can use x = -4 and y = 0 into the equation of the line. In slope-intercept form, that equation is:
[tex]\begin{gathered} y=mx+b\text{ where m is the slope, and b the y-intercept} \\ \\ y=-4x+b \\ \\ 0=-4(-4)+b \\ \\ 0=16+b \\ \\ b=-16 \end{gathered}[/tex]
Therefore, the line passing through (-4, 0) and parallel to the given line has the equation
[tex]y=-4x-16[/tex]
b). And the line perpendicular to the given line has s
