Find the Slope and y-intercept 5x+6y=19

$5 x + 6 y = 19$

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 $5 x$ from both sides of the equation.

$6 y = 19 - 5 x$

Divide each term in $6 y = 19 - 5 x$ by $6$ and simplify.

Divide each term in $6 y = 19 - 5 x$ by $6$ .

$\frac{6 y}{6} = \frac{19}{6} + \frac{- 5 x}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{19}{6} + \frac{- 5 x}{6}$

Divide $y$ by $1$ .

$y = \frac{19}{6} + \frac{- 5 x}{6}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{19}{6} - \frac{5 x}{6}$

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

Reorder $\frac{19}{6}$ and $- \frac{5 x}{6}$ .

$y = - \frac{5 x}{6} + \frac{19}{6}$

Reorder terms.

$y = - (\frac{5}{6} x) + \frac{19}{6}$

Remove parentheses.

$y = - \frac{5}{6} x + \frac{19}{6}$

Step 2

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

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

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

$b = \frac{19}{6}$

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

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

y-intercept: $(0, \frac{19}{6})$

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

y-intercept: $(0, \frac{19}{6})$

Step 3