Question

What is an equation of the line that passes through the point (-2,-3) and is parallel to the line 4x-y=1

Answer 1

y = 4x + 5

Explanation:

First, we need to find the slope of the given equation: 4x - y = 1

Subtract 4x from both sides

4x - y = 1

- 4x - 4x

-y = 1 - 4x

Divide both sides by -1 to make the y variable positive

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

y = -1 + 4x

This means the slope of this equation is 4

Our parallel equation will be y = 4x + b

Plug in the given coordinates

-3 = 4(-2) + b

-3 = -8 + b

Add 8 to both sides

-3 = -8 + b

+ 8 + 8

b = 5

Plug in the new b into the original parallel equation

y = 4x + 5

Answer 2

Answer: y = 4x + 5

Explanation:

Rearranging 4x-y = 1 we get y = 4x-1 as the equation of the line.

Since the new line is parallel to y=4x-1, that means the slopes are equal. Therefore, the slope of the line is 4.

So, the equation of the line is y = 4x+b

To figure out b, we can plug in the point (-2,-3) into the equation.

So -3 = -2*4 + b

-3 = -8 + b

And we get b = 5.

Therefore, the equation of the line is y = 4x + 5