Question

What is the equation of the line that passes through the points (4,3),(6,5)?

Answer 1

`y=x-1`

Skills needed: Point-slope Form

Explanation:

1) First, let's try to make sense out of the problem. We are given two coordinate points and have to create a line out of it.

---> The most efficient way to solve this is with point-slope form.

The point slope form, given One coordinate point and Slope is:

Given coordinate pair
`(x_1, y_1)` and Slope
`m`

--->
`y-y_1=m(x-x_1)`

2) Now, we have one coordinate pair/point, but we need slope.

---> The slope is the rate of change, and can be found with a formula:

Given two coordinate points
`(x_1,y_1)` and
`(x_2, y_2)`, the slope is:

--->
`(y_2-y_1)/(x_2-x_1)`

Let's use this formula for the points above:

`4=x_1, 6=x_2, 3=y_1, 5=y_2`

`(5-3)/(6-4) = (2)/(2) = 1`

Based on the above: Slope = 1 (or
`m=1`)

3) Next, we use point slope form. Let's use coordinate pair (4, 3) -- It does not matter which one:

`y-3=1(x-4)`

The 1 does not mean anything (since anything multiplied by 1 is itself, so it can be taken out:

`y-3=x-4`

Now to get it to slope-intercept form (
`y=mx+b`) ---> We add 3 to both sides

--->
`y-3+3=x-4+3 \\ y=x-1`

y=x-1 is the final equation.

Answer 2

In slope intercept form, the equation would be y = x - 1.

Explanation: