# How do you find the slope and intercept of 7x=5y?

May 25, 2018

The slope is $\frac{7}{5}$ and the y-intercept is $0$.

#### Explanation:

Reverse the equation.

$5 y = 7 x$

Divide both sides by $5$.

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

This equation is in slope-intercept form:

$y = m x + b$,

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

In the equation $y = \frac{7}{5} x$, the slope is $\frac{7}{5}$ and the y-intercept is $0$.

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

May 25, 2018

Slope: $\frac{7}{5}$, Intercepts $\left(0 , 0\right)$

#### Explanation:

$7 x = 5 y \to y = \frac{7}{5} x$

Recall the equation of a straight line in slope $\left(m\right)$ and $y -$intercept $\left(c\right)$ form is: $y = m x + c$

In this example: $m = \frac{7}{5} \mathmr{and} c = 0$

Also, $x = 0$ where $y = 0$

Hence, $y$ is a straight line through the origin with slope $\frac{7}{5}$ as shown below.

graph{7/5x [-11.46, 11.04, -4.785, 6.465]}

So, slope of $y$ is $\frac{7}{5}$ and both $x \mathmr{and} y$ Intercepts occur at the point $\left(0 , 0\right)$