# How do you graph using the intercepts for 2x + 3y = 8?

Jun 11, 2018

The $x$ intercept is the point $\left(4 , 0\right)$

The $y$ intercept is the point $\left(0 , \frac{8}{3}\right)$

Connect the two points to draw the line

#### Explanation:

To look for intercepts means to look for points where a given graph meets one of the axis.

The $x$ axis is the set of all points with coordinates like $\left(x , 0\right)$, i.e. their $y$ coordinate is zero.

Similarly, the $y$ axis is the set of all points with coordinates like $\left(0 , y\right)$, i.e. their $x$ coordinate is zero.

So, if we want to find the $x$ intercept, we need to set $y = 0$ and solve for $x$: the equation becomes

$2 x + 3 \cdot 0 = 8 \setminus \implies 2 x = 8 \setminus \implies x = 4$

So, the $x$ intercept is the point $\left(4 , 0\right)$

Similarly, to find the $y$ intercept we set $x = 0$ and solve for $y$:

$2 \cdot 0 + 3 y = 8 \setminus \implies 3 y = 8 \setminus \implies y = \frac{8}{3}$

So, the $y$ intercept is the point $\left(0 , \frac{8}{3}\right)$

Since the equation we're working on represents a line, it is sufficient to connect the two points we've just found to draw the graph.