Question

Find the equation of the line parallel to y = -2 x + 1 that contains the point ( -3, 4 ). Show your work.

Answer 1

Parallel lines have the same slope.

4 = -2(-3) + b

4 = 6 + b

b = -2

y = -2x - 2

Answer 2

`\mathbf{y=-2x-2}`

Detailed explanation:

Hi there! Our task is to find the equation of the line, given that:

• it's parallel to y = -2x + 1
• it contains the point (-3,4)

Parallel lines have equal slopes, which means that the slope of y = -2x + 2 is equal to the line that's parallel to it.

The slope of y = -2x + 2 is -2.

Hence, the slope of the line that is parallel to it is -2.

Now, find the point-slope equation by plugging in the data:

`\mathbf{y-y_1=m(x-x_1)}`

`\mathbf{y-4=-2(x-(-3)}`

`\mathbf{y-4=-2(x+3)}`

`\mathbf{y-4=-2x-6}`

`\mathbf{y=-2x-6+4}`

`\mathbf{y=-2x-2}`

`\bigstar` Therefore, the equation is y = -2x - 2.