# How do you find the x and y intercepts of 14-3x=7y?

Feb 14, 2017

x-intercept: $- \frac{14}{3} \textcolor{w h i t e}{\text{XXX}}$y-intercept: $2$

#### Explanation:

For all points on the Y-axis, $x = 0$
The y-intercept is the value of $y$ where the graph of the relation crosses the Y-axis.
Stated another way, the y-intercept is the value of $y$ given by the relationship when $x = 0$
If $\textcolor{red}{x} = \textcolor{red}{0}$
then $14 - 3 \textcolor{red}{x} = 7 y$
$\rightarrow 14 = 7 y$
$\rightarrow y = 2$
So the y-intercept is $2$ (that is the point $\left(x , y\right) = \left(0 , 2\right)$)

Similarly the x-intercept is the value of $x$ given by the relationship when $y = 0$
If $\textcolor{b l u e}{y} = \textcolor{b l u e}{0}$
then $14 - 3 x = 7 \textcolor{b l u e}{y}$
$\rightarrow 14 - 3 x = 0$
$\rightarrow x = - \frac{14}{3}$
So the x-intercept is $- \frac{14}{3}$ (that is the point $\left(x , y\right) = \left(- \frac{14}{3} , 0\right)$)