# What are the intercepts of : 5y= 7x - 19?

Mar 9, 2018

$x = \frac{19}{7}$

$y = - \frac{19}{5}$

#### Explanation:

To find the $x$-intercept, we set $y$ equal to $0$ and solve:

$5 \times 0 = 7 \times x - 19$

$19 = 7 x$

$x = \frac{19}{7}$

Now we solve for when $x = 0$ to get the $y$-intercept:

$5 y = 7 \times 0 - 19$

$5 y = - 19$

$y = - \frac{19}{5}$

To check our work, let''s graph the equation and make sure our intercepts are correct

graph{5y = 7x-19}

Yep, we were right!

Mar 9, 2018

$x$ intercept $= \frac{19}{7} , y$ intercept $= - \frac{19}{5}$

#### Explanation:

To find the x-intercept of a given linear equation, plug in 0 for 'y' and solve for 'x'.

To find the y-intercept, plug 0 in for 'x' and solve for 'y'.

Given equation is $5 y = 7 x - 19$

To find x intercept : when y = 0,

$7 x - 19 = \left(5 \cdot 0\right) = 0$

$7 x = 19$ or $x = \frac{19}{7}$

To find y intercept : when x = 0,

$\left(7 \cdot 0\right) - 19 = 5 y$

$5 y = - 19$ or $y = - \frac{19}{5}$

color(purple)(y = (7x-19) / 5
graph{(7x - 19) / 5 [-10, 10, -5, 5]}

Mar 9, 2018

The x-intercept is $\left(\frac{19}{7} , 0\right)$ or $\approx \left(2.714 , 0\right)$.

The y-intercept is $\left(0 , - \frac{19}{5}\right)$ or $\left(0 , - 3.8\right)$.

#### Explanation:

Given:

$5 y = 7 x - 19$

Solve for $y$ to get the equation into slope-intercept form:

$y = m x + b ,$

where:

$m$ is the slope, and $b$ is the y-intercept.

$5 y = 7 x - 19$

Divide both sides by $5$.

$y = \frac{7 x}{5} - \frac{19}{5}$

The y-intercept is the value of $y$ when $x = 0$.

The y-intercept is $\left(0 , - \frac{19}{5}\right)$ or $\left(0 , - 3.8\right)$

The x-intercept is the value of $x$ when $y = 0$.

Substitute $0$ for $y$ and solve for $x$.

$0 = \frac{7 x}{5} - \frac{19}{5}$

Multiply both sides by $5$.

$5 \times 0 = 7 x - 19$

Simplify.

$0 = 7 x - 19$

Add $19$ to both sides.

$19 = 7 x$

Divide both sides by $7$.

$\frac{19}{7} = x$

The x-intercept is $\left(\frac{19}{7} , 0\right) \approx \left(2.714 , 0\right)$

graph{y=7/5x-19/5 [-10, 10, -5, 5]}