1 Answer

Minglyu · Answer 1 · 2021-11-28T10:31:52+0000

Answer:

y=-(5)/(3)x+20

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

Here, the y-intercept is: 20

Thus, option (d) is true.

Explanation:

Given the equation

y=(3)/(5)x+10

comparing the equation with the slope-intercept form

y=mx+b

Here,

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:

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

$y-\left(-5\right)=(-5)/(3)\left(x-15\right)$

$y+5=(-5)/(3)\left(x-15\right)$

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

$y+5=(-5)/(3)\left(x-15\right)$

subtract 5 from both sides

$y+5-5=(-5)/(3)\left(x-15\right)-5$

y=-(5)/(3)x+20

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

Here, the y-intercept is: 20

Thus, option (d) is true.

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