Question

which of these is a point slope equation of the line that is perpendicular to y - 8 = 3(x -10) and passes through -2, 7 A. y - 7 = -1/3 (x+2) B. y - 7 = -3 (x+2) C. y+7=-1/3(x-2) D. Y+7=3(x-2)

Answer 1

A

Explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 8 = 3(x - 10) is in this form

with slope m = 3

Given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(3)`

the line passes through (a, b) = (- 2, 7), hence

y - 7 = -
`(1)/(3)`(x - (- 2)), that is

y - 7 = -
`(1)/(3)`(x + 2) → A

Answer 2

Answer: OPTION A

Explanation:

The form of point slope equation of the line is:

`(y-y_1)=m(x-x_1)`

Where m is the slope and (
`x_1,y_1`) is a poing of the line.

The line given is:

`y-8=3(x-10)`

So the slope of this line is m=3

By definition, if two lines are perpendicular to each other, then theis slopes are opposite reciprocals. Therefore the slope of the other line must be:

`m=-(1)/(3)`

Substituting the slope and the points given into the formula, you obtain that the line is:

`(y-7)=-(1)/(3)(x+2)`