Question

What is the y-intercept of the equation of the line that is perpendicular to the line v= x -x+ 10 and passes through the

Answer 1

Answer:

$y=-\frac{5}{3}x+20$

Here, m=-5/3, and b=y-intercept=20

Here, the y-intercept is: 20

Thus, option (d) is true.

Step-by-step explanation:

Given the equation

$y=\frac{3}{5}x+10$

comparing the equation with the slope-intercept form

$y=mx+b$

Here,

• m is the slope

• y is the intercept

so the slope of the line is 3/5.

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: -5/3

Therefore, the point-slope form of the equation of the perpendicular line that goes through (15,-5) is:

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

$y-\left(-5\right)=\frac{-5}{3}\left(x-15\right)$

$y+5=\frac{-5}{3}\left(x-15\right)$

simplifying the equation to convert it into the slope-intercept form

We know that the slope-intercept form of the line equatio is

$y=mx+b$

here 'm' is the slope and 'b' is the y-intercept

$y+5=\frac{-5}{3}\left(x-15\right)$

subtract 5 from both sides

$y+5-5=\frac{-5}{3}\left(x-15\right)-5$

$y=-\frac{5}{3}x+20$

Here, m=-5/3, and b=y-intercept=20

Here, the y-intercept is: 20

Thus, option (d) is true.