Question

What is the equation of the line in point-slope form and slope-intercept form that is

perpendicular to the line
4x - 3y = 30 and passes through the point (-8, 7)?

Answer 1

9514 1404 393

Answer:

• y -7 = -3/4(x +8)
• y = -3/4x +1

Explanation:

The slope of a line in the form ...

ax +by = c

is ...

m = -a/b

So, the slope of the given line is ...

-4/(-3) = 4/3

The slope of the perpendicular line is the opposite reciprocal of this,

m' = -1/(4/3) = -3/4

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The point-slope equation of a line is ...

y -k = m(x -h) . . . . . . . . line with slope m through point (h, k)

Then your perpendicular line with slope -3/4 through point (-8, 7) is ...

y -7 = -3/4(x +8)

Rearranging to slope-intercept form, we get ...

y = -3/4x -3/4(8) +7

y = -3/4x +1