Find the Slope and y-intercept 3x+4y=17

$3 x + 4 y = 17$

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 $3 x$ from both sides of the equation.

$4 y = 17 - 3 x$

Divide each term in $4 y = 17 - 3 x$ by $4$ and simplify.

Divide each term in $4 y = 17 - 3 x$ by $4$ .

$\frac{4 y}{4} = \frac{17}{4} + \frac{- 3 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{17}{4} + \frac{- 3 x}{4}$

Divide $y$ by $1$ .

$y = \frac{17}{4} + \frac{- 3 x}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{17}{4} - \frac{3 x}{4}$

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

Reorder $\frac{17}{4}$ and $- \frac{3 x}{4}$ .

$y = - \frac{3 x}{4} + \frac{17}{4}$

Reorder terms.

$y = - (\frac{3}{4} x) + \frac{17}{4}$

Remove parentheses.

$y = - \frac{3}{4} x + \frac{17}{4}$

Step 2

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

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

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

$b = \frac{17}{4}$

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

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

y-intercept: $(0, \frac{17}{4})$

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

y-intercept: $(0, \frac{17}{4})$

Step 3