Find the Slope and y-intercept 2x+5y=10

$2 x + 5 y = 10$

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 $2 x$ from both sides of the equation.

$5 y = 10 - 2 x$

Divide each term in $5 y = 10 - 2 x$ by $5$ and simplify.

Divide each term in $5 y = 10 - 2 x$ by $5$ .

$\frac{5 y}{5} = \frac{10}{5} + \frac{- 2 x}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{10}{5} + \frac{- 2 x}{5}$

Divide $y$ by $1$ .

$y = \frac{10}{5} + \frac{- 2 x}{5}$

Simplify the right side.

Simplify each term.

Divide $10$ by $5$ .

$y = 2 + \frac{- 2 x}{5}$

Move the negative in front of the fraction.

$y = 2 - \frac{2 x}{5}$

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

Reorder $2$ and $- \frac{2 x}{5}$ .

$y = - \frac{2 x}{5} + 2$

Reorder terms.

$y = - (\frac{2}{5} x) + 2$

Remove parentheses.

$y = - \frac{2}{5} x + 2$

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

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

$m = - \frac{2}{5}$

$b = 2$

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

Slope: $- \frac{2}{5}$

y-intercept: $(0, 2)$

Slope: $- \frac{2}{5}$

y-intercept: $(0, 2)$