Question

Find an equation of the line that satisfies the given conditions.
Through (5, 3) and (4, 7)

Answer 1

The equation of a line is made up of 4 parts: the y intercept, the slope, y,and x. To find the slope, follow the formula y2-y1/x2-x1. 7-3/4-5 = 4/-1 = -4. Choose either of the ordered pairs to be your x and y. Now you have 3 = -4(5) + b. Solve for b by performing the opposite operation (in this case, add 20 to both to isolate b) and you get b = 23. Put it all together and you get:

y = -4x + 23

Answer 2

First find the slope of the line through those coordinates.

Slope formula:

m = (y2-y1)/(x2-x1)
m=(7-3)/(4-5)
m=4/-1
m=-4
So the slope is -4

Now use the point slope formula:

y-y1=m(x-x1)

y-3 = -4(x-5)
y-3=-4x+20
y=-4x+23

You will get the same result if you use the other coordinates in the point slope formula as well:

y-7=-4(x-4)
y-7=-4x+16
y=-4x+ 23