Find the equation of the line

Question

find the equation of the line. Write the equation using function notation. Through (4,-3) perpendicular to 7y=x-14

Answer 1

7y=x-14

 

Solve for y to put in slope intercept form

 

y = (1/7)x - 2

 

slope = 1/7

 

perpendicular line will have a slope that is

the negative reciprocal... -1/(1/7) = -7

 

You need the equation of a line with

slope m=-7 through point (4, -3)

 

Using point slope form  y-y₁ = m(x-x₁):

 

y - (-3) = -7(x-4)

y + 3 = - 7x + 28

y = -7x + 25

Answer 2

First, find the slope of the line 7y = x-14 by putting the equation in slope-intercept form:  y = (1/7)x - 2.

 

    Slope = 1/7

 

Slope of perpendicular line = -1/(1/7) = -7

 

Equation of line perpendicular to 7y=x-14 and passing through the point (4,-3):  y-(-3) =- 7(x-4)

 

                                                                                                                                  y = -7x+25