A line is parallel to y=-2x+1 and intersects at the point (4,1). What is the equation of this parallel line?

Answer 1

Let's use the point-slope formula to solve this:

y - y₁ = m(x - x₁)

We're told that the line is parallel, so the slope is going to be equal, and we're given the point (4,1)

y - 1 = -2(x - 4)

y - 1 = -2x + 8

add 1 to both sides:

y = -2x + 9

Answer 2

y = -2x + 9

A parallel line will always have the same slope. If you use the slope-intercept equation, y = mx + b, substitute -2 for m, 4 for x, and 1 for y, solve for b, and you'll get the second equation.