Find the Slope and y-intercept 5(2x-3y)=4

$5 (2 x - 3 y) = 4$

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.

$y = m x + b$

Simplify the left side.

Simplify $5 (2 x - 3 y)$ .

Apply the distributive property.

$5 (2 x) + 5 (- 3 y) = 4$

Multiply.

Multiply $2$ by $5$ .

$10 x + 5 (- 3 y) = 4$

Multiply $- 3$ by $5$ .

$10 x - 15 y = 4$

Subtract $10 x$ from both sides of the equation.

$- 15 y = 4 - 10 x$

Divide each term in $- 15 y = 4 - 10 x$ by $- 15$ and simplify.

Divide each term in $- 15 y = 4 - 10 x$ by $- 15$ .

$\frac{- 15 y}{- 15} = \frac{4}{- 15} + \frac{- 10 x}{- 15}$

Simplify the left side.

Cancel the common factor of $- 15$ .

Cancel the common factor.

$\frac{- 15 y}{- 15} = \frac{4}{- 15} + \frac{- 10 x}{- 15}$

Divide $y$ by $1$ .

$y = \frac{4}{- 15} + \frac{- 10 x}{- 15}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{4}{15} + \frac{- 10 x}{- 15}$

Cancel the common factor of $- 10$ and $- 15$ .

Factor $- 5$ out of $- 10 x$ .

$y = - \frac{4}{15} + \frac{- 5 (2 x)}{- 15}$

Cancel the common factors.

Factor $- 5$ out of $- 15$ .

$y = - \frac{4}{15} + \frac{- 5 (2 x)}{- 5 (3)}$

Cancel the common factor.

$y = - \frac{4}{15} + \frac{- 5 (2 x)}{- 5 \cdot 3}$

Rewrite the expression.

$y = - \frac{4}{15} + \frac{2 x}{3}$

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

Reorder $- \frac{4}{15}$ and $\frac{2 x}{3}$ .

$y = \frac{2 x}{3} - \frac{4}{15}$

Reorder terms.

$y = \frac{2}{3} x - \frac{4}{15}$

Step 2

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

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

$m = \frac{2}{3}$

$b = - \frac{4}{15}$

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

Slope: $\frac{2}{3}$

y-intercept: $(0, - \frac{4}{15})$

Slope: $\frac{2}{3}$

y-intercept: $(0, - \frac{4}{15})$

Step 3

Find the Slope and y-intercept 5(2x-3y)=4

Related Questions

Support LCMGCF.com by disabling your adblocker.