Find the Slope and y-intercept 4x-1=3y+5

$4 x - 1 = 3 y + 5$

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.

$y = m x + b$

Rewrite the equation as $3 y + 5 = 4 x - 1$ .

$3 y + 5 = 4 x - 1$

Move all terms not containing $y$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$3 y = 4 x - 1 - 5$

Subtract $5$ from $- 1$ .

$3 y = 4 x - 6$

Divide each term in $3 y = 4 x - 6$ by $3$ and simplify.

Divide each term in $3 y = 4 x - 6$ by $3$ .

$\frac{3 y}{3} = \frac{4 x}{3} + \frac{- 6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{4 x}{3} + \frac{- 6}{3}$

Divide $y$ by $1$ .

$y = \frac{4 x}{3} + \frac{- 6}{3}$

Simplify the right side.

Divide $- 6$ by $3$ .

$y = \frac{4 x}{3} - 2$

Reorder terms.

$y = \frac{4}{3} x - 2$

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

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

$m = \frac{4}{3}$

$b = - 2$

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

Slope: $\frac{4}{3}$

y-intercept: $(0, - 2)$

Slope: $\frac{4}{3}$

y-intercept: $(0, - 2)$