Write an equation in slope intercept form of the line that passes through the given point and is parallel to the graph of the given equation is (1,-3)y+2=4x-1

Answer 1

For lines to be parallel, their slopes must be equal. The slope in the original equation is 4, since it is the coefficient of x. This is the only information we need from the original equation. All we need now is some point that is on the line to tell us where to put this parallel line. It is supposed to contain (1, -3). There are at least 2 ways to add this information.

Method 1: Point-Slope Form

Point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is slope. We have both of these, so we can plug them in, as follows:

y - 1 = 4(x - -3) or y - 1 = 4(x + 3)

Since we need it in slope-intercept form, we solve for y and simplify:

y - 1 = 4x + 12

y = 4x + 13

Method 2: Slope-intercept form

This can also be done using slope-intercept form. In one sense, it is not as direct, but it is a more familiar form. We can plug in 4 for m, and the x and y coordinates can be plugged in for x and y and then solve for b, as follows:

y = mx + b

1 = 4 • -3 + b

1 = -12 + b

13 = b

We can then put the full equation together as y = 4x + 13.