Find the Slope and y-intercept 6x-5y=4

$6 x - 5 y = 4$

Step 1

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Subtract $6 x$ from both sides of the equation.

$- 5 y = 4 - 6 x$

Divide each term in $- 5 y = 4 - 6 x$ by $- 5$ and simplify.

Divide each term in $- 5 y = 4 - 6 x$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{4}{- 5} + \frac{- 6 x}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{4}{- 5} + \frac{- 6 x}{- 5}$

Divide $y$ by $1$ .

$y = \frac{4}{- 5} + \frac{- 6 x}{- 5}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{4}{5} + \frac{- 6 x}{- 5}$

Dividing two negative values results in a positive value.

$y = - \frac{4}{5} + \frac{6 x}{5}$

Write in $y = m x + b$ form.

Reorder $- \frac{4}{5}$ and $\frac{6 x}{5}$ .

$y = \frac{6 x}{5} - \frac{4}{5}$

Reorder terms.

$y = \frac{6}{5} x - \frac{4}{5}$

Step 2

Use the slope-intercept form to find the slope and y-intercept.

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = \frac{6}{5}$

$b = - \frac{4}{5}$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $\frac{6}{5}$

y-intercept: $(0, - \frac{4}{5})$

Slope: $\frac{6}{5}$

y-intercept: $(0, - \frac{4}{5})$

Step 3