Question

Consider the line y = = 8 x-4. Find the equation of the line that is parallel to this line and passes through the point (7, -2). Find the equation of the line that is perpendicular to this line and passes through the point (7, -2). ​

Answer 1

Parallel have same slopes. Perpendicular have opposite reciprocal slopes.

Parallel slope = 8
Perpendicular slope = -1/8

Use point slope. Use point and respective slope.

y-y1= m(x-x1)
y+2 = 8(x-7)
y+2 = 8x - 56
y= 8x - 58 (parallel equation)

y-y1= m(x-x1)
y+2 = -1/8(x-7)
y+2 = -1/8x +7/8
y= -1/8x - 11/8 (perpendicular equation)

Does that help?

Answer 2

Answer: y=8x-58

Explanation:

1. find the slope

Since the new line is parallel to the first one that means the slope of 8x will remain the same.

2. plug it into the point slope formula y-y1=m(x-x1)

which would look like

y-(-2)=8(x-7)

3. solve for y

y-(-2)=8(x-7)

y+2=8x-56

y=8x-58