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

Apr 22, 2015

Slope: $- \frac{2}{3}$
y-intercept: $\left(0 , - 2\right)$

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 $y = m x + b$ form. This is helpful because, when a line is in this form, the slope and y-intercept can immediately be seen. In $y = m x + b$, $m =$ slope, and $b =$ y-intercept value.

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

So in $y = - \frac{2}{3} x - 2 = m x + b$ we can see that $m = - \frac{2}{3}$ 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 $\left(0 , - 2\right)$. The slope (rise/run) goes up 2 and left 3, hence the slope of $- \frac{2}{3}$

Apr 22, 2015

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

Subtract $2 x$ from both sides.

$3 y = - 2 x - 6$

Divide both sides by 3.

$y = - \frac{2}{3} x - \frac{6}{3}$ =

$y = - \frac{2}{3} x - 2$

$y = - \frac{2}{3} x - 2$ is in slope-intercept form, $y = m x + b$. The slope, $m$, is $- \frac{2}{3}$ and the y-intercept, $b$, is $- 2$.

Determine two points on the line.

If $x = 0 , y = - \frac{2}{3} \cdot 0 - 2 = 0 - 2 = - 2$
Point = $\left(0 , - 2\right)$
If $x = 3 , y = - \frac{2}{\cancel{3}} \cdot \cancel{3} - 2 = - 4$
Point = $\left(3 , - 4\right)$

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]}