What is the slope-intercept equation of the line that is perpendicular to y-4=-2/3(x-6) and that passes through (-2, -2)?

Question

asked Jun 14, 2021 147k views

1 Answer

Stefanct · Answer 1 · 2021-06-18T18:11:11+0000

Answer:

The slope-intercept equation is:

y=(3)/(2)x+1

Explanation:

Given the equation

$y-4=-(2)/(3)\left(x-6\right)$

comparing it with the point-slope form of the line equation

$y-y_1=m\left(x-x_1\right)$

where m is the slope

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so

The slope of the perpendicular line will be: 3/2

The point-slope form of the equation of the perpendicular line that goes through (-2, -2) is:

$y-y_1=m\left(x-x_1\right)$

$y-\left(-2\right)=(3)/(2)\left(x-\left(-2\right)\right)$

$y+2=(3)/(2)\left(x+2\right)$

writing the line equation in the slope-intercept form

$y+2=(3)/(2)\left(x+2\right)$

subtract 2 from both sides

$y+2-2=(3)/(2)\left(x+2\right)-2$

y=(3)/(2)x+1

Thus, the slope-intercept equation is:

y=(3)/(2)x+1

Here,

As the slope-intercept form is

y=mx+b

where m is the slope and b is the y-intercept

so

y=(3)/(2)x+1

m=3/2

b = y-intercept = 1

Therefore, the slope-intercept equation is:

y=(3)/(2)x+1