Mathematics, 04.12.2020 20:20, katlynnschmolke

Question: 1. Write an equation of the line that is parallel to y = -4x + 8 and passes through the point (5, 1).
2. Write an equation of the line that is perpendicular to y = -4x + 8 and passes through the point (5,1).

Question:

1. Write an equation of the line that is parallel to y = -4x + 8 and passes through the

Answers: 3

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Answers

answered: haileymaree

Explanation is written below.

Step-by-step explanation:

Given the line

y = -4x + 8

Comparing with the slope-intercept form of the line equation

y=mx+b

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

So, the slope of the line = m = -4

We know that the parallel lines have equal slopes.

Thus, the equation of the line that is parallel to y = -4x + 8 and passes through the point (5, 1), using point slope form

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

Here, m is the slope and (x₁, y₁) is the point

substituting the values m = -4 and the point (5, 1)

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

y-1 = -4 (x - 5)

y-1 = -4x+20

y = -4x+20+1

y = -4x + 21

Given the equation

y = -4x + 8

Comparing with the slope-intercept form of the line equation

y=mx+b

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

So, the slope of the line = m = -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: 1/4

Thus, an equation of the line that is perpendicular to y = -4x + 8 and passes through the point (5,1), using point slope form

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

Here, m is the slope and (x₁, y₁) is the point

substituting the values m = 1/4 and the point (5, 1)

$y-1\:=\:\frac{1}{4}\:\left(x\:-\:5\right)$

Add 1 to both sides

$y-1+1=\frac{1}{4}\left(x-5\right)+1$

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

answered: Guest

{x = -1/2 , y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer: {x = -1/2 , y = -1

answered: Guest

step-by-step explanation:

51/3=17

thus 17 is your answer.

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Question: 1. Write an equation of the line that is parallel to y = -4x + 8 and passes through the p...