Question

A line perpendicular to y = 5x - 2 through (-10,6) slope of the new line: _______ equation: ________

Answer 1

Two lines are perpendicular when the multiplication of their slopes is equal to -1. The slope of y = 5x - 2, is 5, then:

`\begin{gathered} m\cdot5=-1 \\ m=-(1)/(5) \end{gathered}`

Then, the slope of the new line: -1/5

The slope-intercept form of a line is:

y = mx + b

where m is the slope and b is the y-intercept

Replacing with point (-10, 6) and m = -1/5, we get:

6 = (-1/5)(-10) + b

6 = 2 + b

6 - 2 = b

4 = b

Then, the equation is: y = -1/5x + 4