# How do you find slope and intercepts to graph 9x-5y=4?

Jun 20, 2018

$m = \frac{9}{5}$; with points $\left(0 , - \frac{4}{5}\right)$ and $\left(1 , 1\right)$

#### Explanation:

Convert the equation into slope-intercept form by solving for $y$.

$- 5 y = - 9 x + 4$ => subtracting both sides by -9x

$y = \frac{9}{5} x - \frac{4}{5}$ = > dividing by -5

The slope-intercept equation takes the form of $y = m x + b$. The slope $m$ would be the coefficient of x, and the constant $b$, the y-intercept (value of $y$ if $x = 0$), thus yielding: $m = \frac{9}{5}$ and $b = - \frac{4}{5}$.

This gives us one point on the line: $\left(0 , - \frac{4}{5}\right)$.

To get another point on the line, substitute any number for x and solve for y. For ease in graphing, choose an integer close to the first point. For this example, let $x = 1$.

$y = \frac{9}{5} \cdot \left(1\right) - \frac{4}{5}$ => by substitution
$y = \frac{9}{5} - \frac{4}{5} = \frac{5}{5} \mathmr{and} 1$

Thus, point $\left(1 , 1\right)$ also belongs to the line. From here, the two points can be connected, and a line can be formed accordingly.

graph{9x-5y=4 [-2.657, 2.657, -1.328, 1.328]}