Question

What is the equation of the line that goes through (3, 4) and (2, -1) in slope-intercept form?

Answer 1

Let's take the first set of coordinates as (2, -1), where `x_1` = 2, and `y_1` = 2.

Now, let's take the second set of coordinates as (3, 4), where `x_2` = 3, and `y_2` = 4.

The gradient of a line is `m="change in y"/"change in x" = (y_2-y_1)/(x_2-x_1)`

Now, let's put our values in, `m=(y_2-y_1)/(x_2-x_1)=(4-("-"1))/(3-2)=(4+1)/(3-2)=5/1=5`

Our gradient is 5, for every x value we go along by, we go up by 5.

Now, we use `y-y_1=m(x-x_1)` to find the equation of the line. Altough it says `y_1` and `x_1`, any set of coordinates can be used.

For this I'll be using (3,4):
`y-y_1=m(x-x_1)`
`y-4=5(x-3)`
`y=5(x-3)+4=5x-15+4=5x-11`

Proof with (2, -1):
`y=5x-11=5(2)-11=10-11=-1`