Question

What is the equation of the line that is perpendicular to the given line and has an x-intercept of 6?

Answer 1

Y = 4/3 x - 8

100% sure! 

Answer 2

Step 1

Find the slope of the given line

Let

$A(-4,4)\ B(4,-2)$

we know that

the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{-2-4}{4+4}$

$m=\frac{-6}{8}$

$m=-\frac{3}{4}$

Step 2

Find the slope of the line perpendicular to the given line

we know that

if two lines are perpendicular

then

the product of their slopes is equal to minus one

so

$m1*m2=-1$

we have

$m1=-\frac{3}{4}$ ------> slope of the given line

Find the value of m2

$m2=-1/m1$

substitute

$m2=-1/(-3/4)$

$m2=\frac{4}{3}$

Step 3

Find the equation of the line

we know that

the equation of the line into point-slope form is equal to

$y-y1=m(x-x1)$

we have

$m=\frac{4}{3}$

x-intercept is equal to $6$ --------> is the point $(6,0)$

substitute in the formula

$y-0=\frac{4}{3}(x-6)$

$y=\frac{4}{3}x-8$

therefore

the answer is the option

$y=\frac{4}{3}x-8$