Question 265574
Find an equation of the line containing the given pair of points. Express the anser in the form x=a, y=b, or y=mx+b (-3,-3)and (5,5)

The slope of the line between the teo points is the difference in y values divided by the difference in x values:

m = [5-(-3)]/(5-(-3)]
m = 8/8 = 1

The slope intercept form of a line is y = mx + b so the equation for this line in slope-intercept form is:

y = 1*x + b

Since the point (5,5) lies on the line we know that when x=5, y also equals 5 so we can substitute x=5 and y=5 in the equation above and solve for b:

5 = 1*5 + b
b = 0

The equation for the line is then y = 1*x + 0 or y = x.

Notice if we had chosen the other point (-3,-3) we would also have had:

-3 = 1*-3 + b
-3 = -3 + b
b = 0