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3 years ago

Write the standard form of the equation of the line described

Mathematics

1 answer:

tiny-mole [99]3 years ago

8 0

Hello!

First you have to find what y is at when x is -3 in the first equation

y = 5/3(-3) + 2

y = -3

A point of the original line is (-3, -3)

The line we want has to go up 2

To do this we add 2 to the y-intercept part of the equation

y = ? + 2 + 2

Since the line is parallel it has the same slope

y = 5/3x + 2 + 2

Simplify

The answer is y = 5/3 x + 4

Hope this helps!

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3 years ago

Give the following equations determine if the lines are parallel perpendicular or neither

GaryK [48]

In order to determine whether the equations are parallel, perpendicular, or neither, let's simply each equation into a slope-intercept form or basically, solve for y.

Let's start with the first equation.

$\frac{6x-5y}{2}=x+1$

Cross multiply both sides of the equation.

$6x-5y=2(x+1)$ $6x-5y=2x+2$

Subtract 6x on both sides of the equation.

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Divide both sides of the equation by -5.

$-\frac{5y}{-5}=\frac{-4x}{-5}+\frac{2}{-5}$ $y=\frac{4}{5}x-\frac{2}{5}$

Therefore, the slope of the first equation is 4/5.

Let's now simplify the second equation.

$-4y-x=4x+5$

Add x on both sides of the equation.

$-4y-x+x=4x+5+x$ $-4y=5x+5$

Divide both sides of the equation by -4.

$\frac{-4y}{-4}=\frac{5x}{-4}+\frac{5}{-4}$ $y=-\frac{5}{4}x-\frac{5}{4}$

Therefore, the slope of the second equation is -5/4.

Since the slope of each equation is the negative reciprocal of each other, then the graph of the two equations is perpendicular to each other.

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1 year ago

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Karolina [17]

When you see "is the same", that means the left side of the equation equals the right side.
4 times a number. Set up 4x.
Increased by 2. Add 2 to set up 4x + 2.
10 more than 2 times is 2x + 10.
Solve for x: 4x + 2 = 2x + 10
:)

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3 years ago