Find the Slope and y-intercept -1/2x+2y=7

$- \frac{1}{2} x + 2 y = 7$

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.

$y = m x + b$

Simplify the left side.

Combine $x$ and $\frac{1}{2}$ .

$- \frac{x}{2} + 2 y = 7$

Add $\frac{x}{2}$ to both sides of the equation.

$2 y = 7 + \frac{x}{2}$

Divide each term in $2 y = 7 + \frac{x}{2}$ by $2$ and simplify.

Divide each term in $2 y = 7 + \frac{x}{2}$ by $2$ .

$\frac{2 y}{2} = \frac{7}{2} + \frac{\frac{x}{2}}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{7}{2} + \frac{\frac{x}{2}}{2}$

Divide $y$ by $1$ .

$y = \frac{7}{2} + \frac{\frac{x}{2}}{2}$

Simplify the right side.

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{7}{2} + \frac{x}{2} \cdot \frac{1}{2}$

Multiply $\frac{x}{2} \cdot \frac{1}{2}$ .

Multiply $\frac{x}{2}$ by $\frac{1}{2}$ .

$y = \frac{7}{2} + \frac{x}{2 \cdot 2}$

Multiply $2$ by $2$ .

$y = \frac{7}{2} + \frac{x}{4}$

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

Reorder $\frac{7}{2}$ and $\frac{x}{4}$ .

$y = \frac{x}{4} + \frac{7}{2}$

Reorder terms.

$y = \frac{1}{4} x + \frac{7}{2}$

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

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

$m = \frac{1}{4}$

$b = \frac{7}{2}$

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

Slope: $\frac{1}{4}$

y-intercept: $(0, \frac{7}{2})$

Slope: $\frac{1}{4}$

y-intercept: $(0, \frac{7}{2})$