Question

Write an equation of the line passes through (4, 1) and is parallel to y = -2x + 7 40

Answer 1

The given equation is

$y=-2x+7$

Notice that this equation has a slope of -2 because that's the coefficient of x.

It's important to know that parallel lines have equal slopes. So, the new line has a slope of -2 too.

Then, we use the given point (4, 1), the slope -2, and the point-slope formula to find the equation

$\begin{gathered} y-y_1=m(x-x_1) \\ y-1=-2(x-4) \\ y-1=-2x+8 \\ y=-2x+8+7 \\ y=-2x+15 \end{gathered}$

Hence, the equation of the new parallel line is y = -2x + 15.