Find the Slope and y-intercept 2x+4y=6x-y

$2 x + 4 y = 6 x - y$

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.

$y = m x + b$

Move all terms containing $y$ to the left side of the equation.

Add $y$ to both sides of the equation.

$2 x + 4 y + y = 6 x$

Add $4 y$ and $y$ .

$2 x + 5 y = 6 x$

Move all terms not containing $y$ to the right side of the equation.

Subtract $2 x$ from both sides of the equation.

$5 y = 6 x - 2 x$

Subtract $2 x$ from $6 x$ .

$5 y = 4 x$

Divide each term in $5 y = 4 x$ by $5$ and simplify.

Divide each term in $5 y = 4 x$ by $5$ .

$\frac{5 y}{5} = \frac{4 x}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{4 x}{5}$

Divide $y$ by $1$ .

$y = \frac{4 x}{5}$

Reorder terms.

$y = \frac{4}{5} x$

Step 2

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

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

$m = \frac{4}{5}$

$b = 0$

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

Slope: $\frac{4}{5}$

y-intercept: $(0, 0)$

Slope: $\frac{4}{5}$

y-intercept: $(0, 0)$

Step 3