Respuesta :
y=4x+64
Explanation:
Two lines are perpendicular if the product of their slopes is -1.
Step 1: Find the slope of the line a
Line a passes through the points (1,-3) and (9,-5)
[tex]\begin{gathered} \text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{-5-(-3)}{9-1} \\ =\frac{-5+3}{8} \\ =-\frac{2}{8} \\ =-\frac{1}{4} \end{gathered}[/tex]The slope of line a = -1/4
Step 2: Determine the slope of line b.
Let the slope of line b = k
Since the product of the two slopes is -1:
[tex]\begin{gathered} k\times-\frac{1}{4}=-1 \\ k=-1\times-4 \\ k=4 \end{gathered}[/tex]The slope of line b = 4
Step 3: Find the equation of line b.
Line b passes through the point (x1,y1)=(-8,32) and has a slope, m = 4.
Using the slope-point form of the equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]Substitute the given values
[tex]\begin{gathered} y-32=4\mleft(x-\mleft(-8\mright)\mright) \\ y-32=4\mleft(x+8\mright) \\ y-32=4x+32 \\ y=4x+32+32 \\ y=4x+64 \end{gathered}[/tex]The equation of line b is y=4x+64.
