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.