Question

Write the equation of a line that is perpendicular to the given line that passes through the given point.

y-2=7/3(x+5); (-4,9)

Answer 1

First we must find the opposite-reciprocal of the original slope.

current slope:
`(7)/(3)`

new slope:
`-(3)/(7)`

Using the new slope and the given point, we will plug them into slope-intercept form and solve for b, the y-intercept.

`9 = -(3)/(7)(-4) + b\\\\9 = (12)/(7) + b\\\\-(51)/(7) = b`

The y-intercept is
`-(51)/(7)`.

Now, we can write the formula for the new line.

Slope-intercept form:
`y = -(3)/(7)x - (51)/(7)`

Point-slope form:
`y - 9 = -(3)/(7)(x + 4)`