Question

How do you write the equation of a line in slope-intercept form passing through (4, 5) and (6, 8)?

Answer 1

The slope-intercept form is `y=3/2x-1`.

Explanation:

First you need to find the slope using the given information.

The equation to use is:

`m=(y_2-y_1)/(x_2-x_1)`,

where `m` is the slope and `(x_1,y_1)` is one point, and #(x_2,y_2) is the other point.

Let `(4,5)` be point 1, and `(6,8)` be point 2.

Substitute the given values into the equation.

`m=(8-5)/(6-4)`

`m=3/2`

Slope intercept form of linear equation:

`y=mx+b`,

where `m` is the slope and `b` is the y-intercept.

Use one of the points to determine the y-intercept. I am using `(4,5)`, but `(6,8)` will give the same answer.

`5=3/2xx4+b`

Simplify.

`5=12/2+b`

`5=6+b`

Subtract `6` from both sides.

`-1=b`

Slope intercept form of the equation:

`y=3/2x-1`