# How do you find the slope and intercept of y = 4/3x - 3?

Aug 2, 2018

The slope is $\frac{4}{3}$.

The $x$-intercept is at $\left(\frac{9}{4} , 0\right)$.

The $y$-intercept is at $\left(0 , - 3\right)$.

#### Explanation:

$y = \frac{4}{3} x - 3$

This equation is in slope-intercept form:

We know the slope is the value multiplied by $x$, so the slope is $\frac{4}{3}$.

To find the $x -$intercept, plug in $0$ for $y$ and solve for $x$:
$0 = \frac{4}{3} x - 3$

Add $\textcolor{b l u e}{3}$ to both sides:
$0 \quad \textcolor{b l u e}{+ \quad 3} = \frac{4}{3} x - 3 \quad \textcolor{b l u e}{+ \quad 3}$

$3 = \frac{4}{3} x$

Multiply both sides by $\textcolor{b l u e}{\frac{3}{4}}$:
3 color(blue)(*3/4) = 4/3x color(blue(*3/4)

$\frac{9}{4} = x$

$x = \frac{9}{4}$

Therefore, the $x$-intercept is at $\left(\frac{9}{4} , 0\right)$.

To find the $y$-intercept, plug in $0$ for $x$ and solve for $y$:
$y = \frac{4}{3} \left(0\right) - 3$

$y = 0 - 3$

$y = - 3$

Therefore, the $y$-intercept is at $\left(0 , - 3\right)$.

Hope this helps!

Aug 2, 2018

Slope $\frac{4}{3}$, $x$-int $\frac{9}{4}$, $y$-int $- 3$

#### Explanation:

This equation is in slope-intercept form

$y = m x + b$, with slope $m$ and a $y$-intercept of $b$. By pattern matching, we see our slope is $\frac{4}{3}$ and our $y$-intercept is $- 3$.

We can find the $x$-intercept by setting $y$ equal to zero. We get

$0 = \frac{4}{3} x - 3 = \frac{4}{3} x = 3 \implies x = \frac{9}{4}$

Therefore, our slope is $\frac{4}{3}$, our $y$-intercept is $- 3$, and our $x$-intercept is $\frac{9}{4}$.

Hope this helps!