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.
Please mark my answers as the Brainliest if you find my explanations helpful :)
