Question

PLEASE HELP ME THIS IS DUE RIGHT NOW HELP ASAP

Answer 1

Step-by-step explanation:

the slope of a line is the ratio

y coordinate change / x coordinate change

when going from one point on the line to another.

so for (-3, 17) and (2, -3) we get

x changes by +5 (from -3 to 2).

y changes by -20 (from 17 to -3).

the slope is

-20/+5 = -4/1 = -4

now, a perpendicular slope (90° to the original slope) is putting the slope fraction upside-down and flips the sign :

+1/4 or simply 1/4.

the slope in an equation of the form "y = ..." is always the factor of x.

y + 2 = (1/4)(x - 1)

yes, there are only some constant additions or subtractions to get to a or "y = ..." form, so 1/4 is indeed the factor of x and the slope of this line.

y = 4x + 12

4 <> 1/4, so, no, it is not.

4x + y = -8

y = -4x - 8

-4 <> 1/4, so, no, it is not.

x - 4y = 2

-4y = -x + 2

y = (1/4)x - 2/4

1/4 is indeed 1/4, so, yes, it is.

y = (1/4)x - 15

1/4 is indeed 1/4, so, yes, it is.

y + 3 = 4(x - 2)

similar to the first one, but 4 <> 1/4, so, no, it is not.

y = -4x + 3

-4 <> 1/4, so, no, it is not.

Answer 2

Answers: A, D, and E

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Step-by-step explanation:

We'll need to find the slope of the line through the two given points.

`(x_1,y_1) = (-3,17) \text{ and } (x_2,y_2) = (2,-3)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_(2) - \text{y}_(1)}{\text{x}_(2) - \text{x}_(1)}\\\\m = (-3 - 17)/(2 - (-3))\\\\m = (-3 - 17)/(2 + 3)\\\\m = (-20)/(5)\\\\m = -4\\\\`

The slope is -4.

Think of -4 as -4/1. The reciprocal is -1/4, and it flips in sign to +1/4 or simply 1/4.

The original slope -4 leads to the perpendicular slope 1/4. The two slopes multiply to -1. This is true of any perpendicular lines where neither is vertical nor horizontal.

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In short, the answer equation will involve a slope of 1/4. This points us directly to choices A and E as two answers so far.

Something like choice B is not an answer since it has slope 4. Choice C is ruled out because 4x+y = -8 solves to y = -4x-8. It has a slope of -4.

Choice D on the other hand has x-4y = 2 solve to y = (1/4)x - 1/2, and this has a slope of 1/4 that we want. This means choice D is another answer.

Choice F and choice G are ruled out because they involve slopes of 4 and -4 respectively.

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Summary: The 3 answers are choices A, D and E