How do you find the x and y intercepts for y=3x-2?

Apr 12, 2018

$y = - 2$
$x = 0$
$\left(0 , - 2\right)$

Explanation:

$y = 3 x - 2$
to
$y + 2 = 3 x$

Next, instead of $x$, put $y + 2$.
$y + 2 = 3 \left(y + 2\right)$

Then, multiply $3$ by $y$ and $3$ by $2$.
$y + 2 = 3 y + 6$

Subtract $y$ from both sides.
$2 + y = 3 y + 6$
to
$2 = 2 y + 6$

Subtract $6$ from both sides.
$2 = 2 y + 6$
to
$- 4 = 2 y$

Divide both sides by $2$.
$- 4 = 2 y$
to
$- 2 = y$
Go back to the original equation. Replace $y$ with $- 2$.
$y = 3 x - 2$
to
$- 2 = 3 x - 2$

Add $2$ to both sides.
$- 2 = 3 x - 2$
to
$0 = 3 x$

Divide both sides by $3$.
$0 = 3 x$
to
$0 = x$

Hope that helped! : )

Apr 12, 2018

The x-intercept is $\left(\frac{2}{3} , 0\right)$.

The y-intercept is $\left(0 , - 2\right)$.

Explanation:

Given:

$y = 3 x - 2$

X-intercept: value of $x$ when $y = 0$.

Substitute $0$ for $y$.

$0 = 3 x - 2$

Add $2$ to both sides.

$2 = 3 x$

Divide both sides by $3$.

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

The x-intercept is $\left(\frac{2}{3} , 0\right)$.

Y-intercept: value of $y$ when $x = 0$

$y = 3 x - 2$ is the slope-intercept form for a linear equation:

$y = m x + b$,

where:

$m$ is the slope, and $b$ is the y-intercept.

Therefore, the y-intercept is $\left(0 , - 2\right)$.

You can also substitute $2$ for $x$ and solve for $y$.

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

$y = - 2$

The y-intercept is $\left(0 , - 2\right)$.

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