Find the Slope -4x+7=2y-3

$- 4 x + 7 = 2 y - 3$

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.

$y = m x + b$

Rewrite the equation as $2 y - 3 = - 4 x + 7$ .

$2 y - 3 = - 4 x + 7$

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

Add $3$ to both sides of the equation.

$2 y = - 4 x + 7 + 3$

Add $7$ and $3$ .

$2 y = - 4 x + 10$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

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

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

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

Cancel the common factors.

Factor $2$ out of $2$ .

$y = \frac{2 (- 2 x)}{2 (1)} + \frac{10}{2}$

Cancel the common factor.

$y = \frac{2 (- 2 x)}{2 \cdot 1} + \frac{10}{2}$

Rewrite the expression.

$y = \frac{- 2 x}{1} + \frac{10}{2}$

Divide $- 2 x$ by $1$ .

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

Divide $10$ by $2$ .

$y = - 2 x + 5$

Step 2

Using the slope-intercept form, the slope is $- 2$ .

$m = - 2$

Step 3