Find the Slope and y-intercept 7x-6y=3

$7 x - 6 y = 3$

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 $7 x$ from both sides of the equation.

$- 6 y = 3 - 7 x$

Divide each term in $- 6 y = 3 - 7 x$ by $- 6$ and simplify.

Divide each term in $- 6 y = 3 - 7 x$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{3}{- 6} + \frac{- 7 x}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{3}{- 6} + \frac{- 7 x}{- 6}$

Divide $y$ by $1$ .

$y = \frac{3}{- 6} + \frac{- 7 x}{- 6}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $3$ and $- 6$ .

Factor $3$ out of $3$ .

$y = \frac{3 (1)}{- 6} + \frac{- 7 x}{- 6}$

Cancel the common factors.

Factor $3$ out of $- 6$ .

$y = \frac{3 \cdot 1}{3 \cdot - 2} + \frac{- 7 x}{- 6}$

Cancel the common factor.

$y = \frac{3 \cdot 1}{3 \cdot - 2} + \frac{- 7 x}{- 6}$

Rewrite the expression.

$y = \frac{1}{- 2} + \frac{- 7 x}{- 6}$

Move the negative in front of the fraction.

$y = - \frac{1}{2} + \frac{- 7 x}{- 6}$

Dividing two negative values results in a positive value.

$y = - \frac{1}{2} + \frac{7 x}{6}$

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

Reorder $- \frac{1}{2}$ and $\frac{7 x}{6}$ .

$y = \frac{7 x}{6} - \frac{1}{2}$

Reorder terms.

$y = \frac{7}{6} x - \frac{1}{2}$

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

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

$m = \frac{7}{6}$

$b = - \frac{1}{2}$

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

Slope: $\frac{7}{6}$

y-intercept: $(0, - \frac{1}{2})$

Slope: $\frac{7}{6}$

y-intercept: $(0, - \frac{1}{2})$