What is the equation of the line that is parallel to y=6x−1 and passes through the point (−3,4)? The equation will be in slope-intercept form.

Answer 1

There are 2 ways to do this, both using the slope of 6, which would give us a line parallel to the given graph.

1. y = mx + b

4 = 6(-3) + b

4 = -18 + b

b = 22

y = 6x + 22

2. y - y₁ = m(x - x₁)

y - 4 = 6(x - (-3))

y - 4 = 6x + 18

y = 6x + 22

Answer 2

Since the line is parallel to the given line, the slopes must be equal. From the given equation, which is already in slope-intercept form, the slope is 6, so we start "building" the new equation with a slope of 6 which becomes y = 6x + b. Now we need to find the "b" value so that we can complete the equation. Since the other line passes through ( -3, 4 ), we insert the x-coordinate of -3 in for "x" in the equation and the y-coordinate of 4 in for "y" in the equation and we solve for b. So the equation we are building becomes 4 = 6(-3) + b. Solving for b, we have b = 22. Now we complete the equation with the slope of 6 and the b value of 22,so the equation is y = 6x + 22.