Mathematics: Write the slope-intercept form of the equation of the line described.

This ia a right answers x=6+2y...

Write the slope-intercept form of the equation

Ответ:

u8p4

12.02.2022

Mathematics

Please check the explanation.

Step-by-step explanation:

Given the line

$y=-\frac{1}{3}x+3$

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

y=mx+b

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

Thus, the slope of line = -1/3

We know that parallel lines have the same slope.

Hence, the slope of the parallel line is also m=-1/3

So, substituting m = -1/3 and (3, 1) in the slope-intercept form to find the y-intercept

y=mx+b

$1=\frac{-1}{3}\left(3\right)+b$

Switch sides

$\frac{-1}{3}\left(3\right)+b=1$

-1+b=1

b=2

Thus, the equation line in slope-intercept form

y=mx+b

$y=-\frac{1}{3}x+2$

Given the line

$y=\frac{1}{4}x+1$

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

y=mx+b

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

so the slope of line = 1/4

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: -4

Thus, subtituting m = -4 and (-1, 4) in the point-slope form

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

$y-4=-4\left(x-\left(-1\right)\right)$

writing the point-slope form in the slope-intercept form

$y-4=-4\left(x+1\right)$

add 4 to both sides

$y-4+4=-4\left(x+1\right)+4$

y=-4x

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Write the slope-intercept form of the equation of the line described.

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