Find the Slope and y-intercept x+4y=16

$x + 4 y = 16$

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 $x$ from both sides of the equation.

$4 y = 16 - x$

Divide each term in $4 y = 16 - x$ by $4$ and simplify.

Divide each term in $4 y = 16 - x$ by $4$ .

$\frac{4 y}{4} = \frac{16}{4} + \frac{- x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{16}{4} + \frac{- x}{4}$

Divide $y$ by $1$ .

$y = \frac{16}{4} + \frac{- x}{4}$

Simplify the right side.

Simplify each term.

Divide $16$ by $4$ .

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

Move the negative in front of the fraction.

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

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

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

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

Reorder terms.

$y = - (\frac{1}{4} x) + 4$

Remove parentheses.

$y = - \frac{1}{4} x + 4$

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

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

$m = - \frac{1}{4}$

$b = 4$

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

Slope: $- \frac{1}{4}$

y-intercept: $(0, 4)$

Slope: $- \frac{1}{4}$

y-intercept: $(0, 4)$