Question

How do you find the slope and y intercept and graph `2x+3y=-6`?

Answer 1

Answer

Slope: `-2/3`
y-intercept: `(0,-2)`

Explanation

There are two simple ways to solve this problem:
1) Algebra
2) Graphing
Let's look at both

1) We can turn the question into the slope-intercept `y=mx+b` form. This is helpful because, when a line is in this form, the slope and y-intercept can immediately be seen. In `y=mx+b`, `m=` slope, and `b=` y-intercept value.

We have to solve for `y` in
`2x+3y=-6`
We need `y` alone. Let's first take `2x` to the other side by subtracting it.
`3y=-6-2x`
Now, we just have to divide by `3` to get the form `y=mx+b`
`y=-6/3-2/3x= -2-2/3x= -2/3x-2`

So in `y=-2/3x-2=mx+b` we can see that `m=-2/3` and `b=-2`

2) We can also graph this function and observe.

graph{-2/3x-2 [-10, 10, -5, 5]}

As you can see, the line intersects the y-axis at `(0,-2)`. The slope (rise/run) goes up 2 and left 3, hence the slope of `-2/3`

Answer 2

Solve `2x+3y=-6` for `y`.

Subtract `2x` from both sides.

`3y=-2x-6`

Divide both sides by 3.

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

`y=-2/3x-2`

`y=-2/3x-2` is in slope-intercept form, `y=mx+b`. The slope, `m`, is `-2/3` and the y-intercept, `b`, is `-2`.

Determine two points on the line.

If `x=0, y=-2/3*0-2=0-2=-2`
Point = `(0,-2)`
If `x=3, y=-2/cancel(3)*cancel(3)-2=-4`
Point = `(3,-4)`

Plot the points and draw a straight line through the two points.
graph{y=-2/3x-2 [-14.24, 14.23, -7.12, 7.12]}