# What is an equation of the the line that passes through the point (-1,4) and is parallel to the line x+y=4

more_vert
What is an equation of the the line that passes through the point (-1,4) and is parallel to the line x+y=4

more_vert

done_all

Solution:

x + y = 4

y = -x + 4 Slope = -1

Equation of line:

y = mx + b

y = (-1)x + b

4 = (-1)(-1) + b Solve for "b" by using given point.

4 = 1 + b

3 = b

Equation: y = (-1)x + 3

more_vert

First, you need to know the slope so rewrite the equation for the line as y = -x + 1. Then remember when the equation in “y = mx + b” form, the slope is always the number m in front of x. So in this cae the slope is -1.

Now there are two ways to get the answer. First, by using “y = mx + b” form, we know m is -1 so only need b. To get b, plug in the (x,y) coordinates for the point (-1,4) like this: (4) = -1*(-1) + b. Remember to plug in the y-coordinate 4 on the left side, and the x number -1 on the right. From this, we see b = 3.

So the final answer is y = -1x + 3.

Another way: besides the “y = mx + b” form, another important form for writing an equation for a line is called the “point-slope” form. It looks like this: given a specified point (a,b) and a specified slope m, then the equation for the line is: y − b = m(x – a).

So for this case: y – 4 = -1(x – (-1)) = -1(x + 1) = -1x – 1. Now bring the 4 over to the other side to get:

y = -x + 3.