which equation represents a line that passes through (3,1) (6,6)

Answer 1

When you are given two coordinates you have to first find the change in y and the change in x, which is your slope. The change in y is 5 since the first y coordinate is 1 and the second y coordinate is 6 (6 - 1 = 5)

The change in x is 3 since the first x coordinate is 3 and the second x coordinate is 6. (6 - 3 = 3)

This means that your slope (m) is 5/3

Then you pick one coordinate and plug in x and y with m to the linear equation format y = mx + b:

I am going to use (3,1): 1 = 5/3(3) + b

Then you solve for b. When multiplying a fraction to a whole number you just multiply to the numerator since 5 is the same as 5/1 and when you multiply fractions you go straight across. This means that:

1 = 15/3 + b

15/3 = 5, so 1 = 5 + b

-5 -5

-4 = b

When you write your final linear equation you only plug in m (slope) and b (y intercept):

y = 5/3x - 4