Question

Write the slope-intercept form of the line that passes through (1, -2) and is parallel to the line y = 4x + 2.

Answer 1

Use

y-y1=m(x-x1)

y-(-2)=4(x-1) Now why 4??Because parallel lines have the exact same slope

y+2=4x-4

y=4x-4-2

y=4x-6

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Answer 2

Parallel lines have the same slope.

Given the linear equation, y = 4x + 2:

Since the slope = 4, then we can assume that the slope of the line parallel to y = 4x + 2 will have the same slope.

We’ll use this slope and the given point, (1,-2), and plug these values into the slope-intercept form (y = mx + b) to solve for the y-intercept (b):

y = mx + b
-2 = 4(1) + b
-2 = 4 + b

Subtract 4 from both sides to isolate and solve for b:

-2 - 4 = 4 - 4 + b
-6 = b

Therefore, the y-coordinate of the y-intercept is -6 . Now, we can finally establish the linear equation of the line parallel to y = 4x + 2, which is:

y = 4x - 6.

Attached is a screenshot of the graph of both equations to show that we came up with a line parallel to the original equation.

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