What is the y-intercept of the line 2x-3y = -6?

Jan 31, 2016

The y-intercept is the point on the y-axis where the line crosses. The y-axis is the line $x = 0$, so substitute in $0$ for $x$ and solve. The y-intercept is $y = 2$.

Explanation:

The y-axis is the line $x = 0$. Substitute in $0$ for $x$ in the equation to find the y-intercept:

$2 x - 3 y = - 6$

$2 \left(0\right) - 3 y = - 6$

$- 3 y = - 6$

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

The y-intercept is simply $y = 2$.

Jan 31, 2016

The answer is, in coordinate-pair format: $\left(0 , 2\right)$

Explanation:

The $y$-intercept is the value of $y$ when $x = 0$.

That means to solve this we should replace $x$ with $0$ and solve for $y$.

Now the equation looks lie this $2 \left(0\right) - 3 y = - 6$.
From here, I would solve $2 x \cdot 0$, which is $0$. The equation is now $- 3 y = - 6$, and from here I would divide both sides by $- 3$. The updated version of the equation is $y = - \frac{6}{-} 3$,or $y = 2$.

We can also graph the equation and check where the $y$-intercept is.

graph{-6=2x-3y}
In this case, it is at (0, 2), which is what we found. We were right!