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

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asked Apr 27, 2023 220k views

1 Answer

Alexander Vogt · Answer 1 · 2023-05-02T02:50:45+0000

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