Question

Line a is perpendicular to line bLine a passes through the points (1,-3) and (9,-5)Line b passes through the point (-8,32)The equation of line b is y=___

Answer 1

y=4x+64

Step-by-step 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)

`\begin{gathered} \text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =(-5-(-3))/(9-1) \\ =(-5+3)/(8) \\ =-(2)/(8) \\ =-(1)/(4) \end{gathered}`

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:

`\begin{gathered} k*-(1)/(4)=-1 \\ k=-1*-4 \\ k=4 \end{gathered}`

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:

`y-y_1=m(x-x_1)`

Substitute the given values

`\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}`

The equation of line b is y=4x+64.