Find the Slope and y-intercept 2x-4y=10

$2 x - 4 y = 10$

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 $2 x$ from both sides of the equation.

$- 4 y = 10 - 2 x$

Divide each term in $- 4 y = 10 - 2 x$ by $- 4$ and simplify.

Divide each term in $- 4 y = 10 - 2 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{10}{- 4} + \frac{- 2 x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{10}{- 4} + \frac{- 2 x}{- 4}$

Divide $y$ by $1$ .

$y = \frac{10}{- 4} + \frac{- 2 x}{- 4}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $10$ and $- 4$ .

Factor $2$ out of $10$ .

$y = \frac{2 (5)}{- 4} + \frac{- 2 x}{- 4}$

Cancel the common factors.

Factor $2$ out of $- 4$ .

$y = \frac{2 \cdot 5}{2 \cdot - 2} + \frac{- 2 x}{- 4}$

Cancel the common factor.

$y = \frac{2 \cdot 5}{2 \cdot - 2} + \frac{- 2 x}{- 4}$

Rewrite the expression.

$y = \frac{5}{- 2} + \frac{- 2 x}{- 4}$

Move the negative in front of the fraction.

$y = - \frac{5}{2} + \frac{- 2 x}{- 4}$

Cancel the common factor of $- 2$ and $- 4$ .

Factor $- 2$ out of $- 2 x$ .

$y = - \frac{5}{2} + \frac{- 2 (x)}{- 4}$

Cancel the common factors.

Factor $- 2$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Reorder terms.

$y = \frac{1}{2} x - \frac{5}{2}$

Step 2

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

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

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

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

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: $(0, - \frac{5}{2})$

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

y-intercept: $(0, - \frac{5}{2})$

Step 3

Find the Slope and y-intercept 2x-4y=10

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