Question

What is the equation of the line passing through `(-3, 2)` and `(3,6)`?

Answer 1

The slope is `2/3`.

Explanation:

First, start with your equation to find slope with two ordered pairs:

`(Y_2 - Y_1)/(X_2 - X_1)` = `m`, where `m` is the slope

Now, label your ordered pairs:

`(-3, 2) (X_1, Y_1)`
`(3, 6) (X_2, Y_2)`

Next, plug them in:

`(6 - 2)/(3 - -3)` = `m`

Simplify. 3 - - 3 becomes 3 + 3 because two negatives create a positive.

`(6 - 2)/(3 + 3)` = `m`

`(4)/(6)` = `m`

Simplify.

`2/3` = `m`

Answer 2

`y=2/3x+4`

Explanation:

First, in order to find the gradient of the line, use the equation `m=(y-y_1)/(x-x_1)`
which would give us `m=(6-2)/(3-(-3)) = 2/3`

Then substitute the gradient (m) into the equation of a line `y=mx+c`

`y = 2/3x+c`

In order to find c (the y-intercept), substitute the coordinates into the equation.

using (3,6)
`(6) = 2/3 (3) +c`

`6= 2 + c`

`6-2 = c`

therefore, `c = 4`

or

using (-3,2)
`(2) = 2/3(-3) + c`

`2= -2 + c`
therefore, `c= 4`

Hence, equation of the line is `y = 2/3x + 4`

Answer 3

Slope-intercept form:

`y=2/3x+4`

Explanation:

First find the slope by using the following equation:

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

where:

`m` is the slope and `(x_1,y_1)` and `(x_2,y_2)` are the two points.

Point 1: `(-3,2)`

Point 2: `(3,6)`

Plug in the known values and solve.

`m=(6-2)/(3-(-3))`

`m=4/6`

Simplify.

`m=2/3`

Use the point-slope formula of a linear equation. You will need the slope and one of the points given in the question.

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

where:

`m` is the slope and `(x_1,y_1)` is the point.

I'm going to use `(-3,2)` for the point.

`y-2=2/3(x-(-3))`

`y-2=2/3(x+3)`

You can convert the point-slope form to slope-intercept form by solving for `y`.

`y=mx+b`,

where:

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

`y=2/3(x+3)+2`

Expand.

`y=2/3x+6/3+2`

Simplify `6/3` to `2`.

`y=2/3x+2+2`

`y=2/3x+4`

graph{y-2=2/3(x+3) [-10.08, 9.92, -3.64, 6.36]}