# How do you find the intercepts for y=3/4x + 4?

Jul 24, 2015

y intercept $= 4$
x intercept $= - \frac{16}{3}$

#### Explanation:

The y-intercept is the value of $y$ when $x = 0$
$\textcolor{w h i t e}{\text{XXXX}}$Setting $x = 0$ in the given equation:
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$y = \frac{3}{4} \left(0\right) + 4$

$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$y = 4$

The x-intercept is the value of $x$ when $y = 0$
$\textcolor{w h i t e}{\text{XXXX}}$Re-writing $y = \frac{3}{4} x + 4$ as an expression for $x$ in terms of $y$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{4}{3} \left(y - 4\right)$

$\textcolor{w h i t e}{\text{XXXX}}$Setting $y = 0$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{4}{3} \left(0 - 4\right)$

$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$x = - \frac{16}{3}$