# How do you find the x and y intercepts and slope if they exist and graph the line -2x + 7y = 14?

Jun 20, 2018

The x intercept is where $y = 0$ or $- 2 x = 14$ so is $x = - 7.$

For the slope and y intercept we write $7 y = 2 x + 14$ or $y = \frac{2}{7} x + 2$ and read off the slope of $\frac{2}{7}$ and y intercept at $y = 2.$

Jun 20, 2018

$y$ intercept: $\left(0 , 2\right)$

$x$ intercept: $\left(- 7 , 0\right)$

Slope: $\frac{2}{7}$

#### Explanation:

To find the intercepts, set one of the coordinates to zero and solve for the other:

$y$ intercept: (set $x = 0$)

$- 2 x + 7 y = 14 \setminus \to 7 y = 14 \setminus \to y = 2$

So, the $y$ intercept is $\left(0 , 2\right)$

$x$ intercept: (set $x = 0$)

$- 2 x + 7 y = 14 \setminus \to - 2 x = 14 \setminus \to x = - 7$

So, the $x$ intercept is $\left(- 7 , 0\right)$

To find the slope, it is convenient to write the equation in the form

$y = m x + q$

once this is done, the slope will be $m$. To reach or goal, let's add $2 x$ to both sides to get

$- 2 x + 7 y = 14 \setminus \to 7 y = 2 x + 14$

and finally divide both sides by $7$ to get

$y = \frac{2}{7} x + 2$

So, the slope is $\frac{2}{7}$