Question

Please help me with these 2 questions :(

Answer 1

Problem 1

Answer: y = -2x-3

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Step-by-step explanation:

Parallel lines have equal slopes but different y intercepts.

Linear equations in the form y = mx+b have slope m and y intercept b.

The slope of y = -2x-4 is m = -2

So any parallel line to this will also have m = -2

Plug (x,y) = (-1,-1) along with the value of m, into y = mx+b and solve for b

y = mx+b

-1 = -2(-1)+b

-1 = 2+b

2+b = -1

b = -1-2

b = -3

The parallel line is y = -2x-3

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Problem 2

Answer: y = -2x-13

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Step-by-step explanation:

We'll use the same ideas and steps as problem 1.

y = -2x-5 has slope m = -2

The parallel line also has slope m = -2

We want the parallel line to go through (x,y) = (-4,-5)

So,

y = mx+b

-5 = -2(-4)+b

-5 = 8+b

8+b = -5

b = -5-8

b = -13

The parallel line is y = -2x-13

Answer 2

1st: y=-2x-3

2nd:y=-2x-13

Step-by-step explanation:

Since the line is parallel to y = -2x-4, its slope is -2. Therefore, we have the equation y=-2x

But when we evaluate that equation at -1, we get -2(-1)=2, but we want to make it equal to -1 when evaluated at -1. Therefore, we can subtract 3, as 2-3=-1.

Therefore, the equation is y=-2x-3.

For the second question, we can use a similar concept. The slope will be -2, but if you directly evaluate it at -4, it's going to be 8, but we want it to be -5, so we subtract 13.

Therefore, the equation is y=-2x-13