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# Slopes!! PLS Help!

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1.Which of the following lines is parallel with the graph of the given equation AND goes through the given point below?

y=8x+2 Point (1,9)

A. y=8x+2

B. y=8x-1

C. y=8x+1

D.y=8x+5

2.Which of the following lines is perpendicular with the graph of the given equation AND goes through the given point below?

-3x+2y-5=7 Point (-3,4)

A.y=2/3x+3

B.y=-2/3x+2

C.y=-2/3x-2

D. y=3/2x-6

Thanks So Much!

May 6, 2021

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1. Which of the following lines is parallel with the graph of the given equation AND goes through the given point below?

y = 8x + 5

Point (1,9)

The answer would be C because parallel lines must have the same slope and the slope needs to be 8. C fits that description but so does everything else, so we need to figure out the y-intercept. Because the slope is 8, or 8/1, for every 1 change in x, there will be 8 changes in y. So, because (1,9) is the point given, we can subtract one from the x and we'll have to subtract 8 from the y. Therefore, our new point will be (0,1) which means our y-intercept is 1. C is the only answer choice that fits this.

2. Which of the following lines is perpendicular with the graph of the given equation AND goes through the given point below?

-3x + 2y - 5 = 7

Point (-3,4)

First, let us put this into slope-intercept form. That will give us:

-3x + 2y - 5 = 7

-3x + 2y = 12

2y = 3x + 12

(Divide both sides by 2)

y = 3/2x + 6

Therefore, our slope is 3/2 and our y-intercept is 6. Now, because we want to find a line perpendicular to this line, we must find the negative reciprocal of the slope, or -2/3. This will be the slop we want. Now, choices B and C fit the description, so we need to find the y-intercept of our new line. We have the point (-3,4) so, because our slope is -2/3, we can add three to the x axis and subtract 2 from the y. So, our new y-intercept is (0,2). Therefore, we need a +2 at the end of our new equation for the line. So the answer would be B.