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

Answer: OPTION A

Step-by-step 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:

$m=-\frac{1}{3}$

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

 $(y-7)=-\frac{1}{3}(x+2)$

Answer 2

Answer:

A

Step-by-step 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

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{3}$

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

y - 7 = - $\frac{1}{3}$(x - (- 2)), that is

y - 7 = - $\frac{1}{3}$(x + 2) → A