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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

(Add 5 to both sides)

-3x + 2y = 12

(Add 3x to both sides)

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.

 

 

 

Answer key:

 

1) C

2) B

6 may. 2021