Find the Slope and y-intercept 5x-10y=20

$5 x - 10 y = 20$

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.

$- 10 y = 20 - 5 x$

Divide each term in $- 10 y = 20 - 5 x$ by $- 10$ and simplify.

Divide each term in $- 10 y = 20 - 5 x$ by $- 10$ .

$\frac{- 10 y}{- 10} = \frac{20}{- 10} + \frac{- 5 x}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 y}{- 10} = \frac{20}{- 10} + \frac{- 5 x}{- 10}$

Divide $y$ by $1$ .

$y = \frac{20}{- 10} + \frac{- 5 x}{- 10}$

Simplify the right side.

Simplify each term.

Divide $20$ by $- 10$ .

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

Cancel the common factor of $- 5$ and $- 10$ .

Factor $- 5$ out of $- 5 x$ .

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

Cancel the common factors.

Factor $- 5$ out of $- 10$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Reorder terms.

$y = \frac{1}{2} x - 2$

Step 2

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

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

$m = \frac{1}{2}$

$b = - 2$

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

Slope: $\frac{1}{2}$

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

Slope: $\frac{1}{2}$

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

Step 3

Find the Slope and y-intercept 5x-10y=20

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