Question

How do I find the equation of a linear function that passes through `(1, 7)` and `(2, 9)`?

Answer 1

For this type of problem we have 3 distinct steps to follow.

1) Find the slope using the formula `m=((y_2-y_1))/((x_2-x_1))`

2) Find the y-intercept, `b`, by substituting in the slope , `m`, from STEP 1 and the `x` and `y` values from one of the points given in the slope intercept formula, `y=mx+b`

3) Substitute the slope, `m`, and the y-intercept, `b`, back into the slope intercept formula, `y=mx+b`.

STEP 1

`x_1=1`
`y_1=7`

`x_2=2`
`y_2=9`

`m=((y_2-y_1))/((x_2-x_1))=((9-7))/((2-1))=2/1=2`

STEP 2

`y=mx+b`

I will use the `x` and `y` values from the point `(1,7)`

`7=(2)(1)+b`
`7=2+b`
`5=b`

STEP 3

`y=mx+b`

`y=2x+5 larr SOLUTION`