Find the Slope and y-intercept 2X-5Y=10

$2 X - 5 Y = 10$

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.

$y = m x + b$

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

$- 5 Y = 10 - 2 X$

Divide each term in $- 5 Y = 10 - 2 X$ by $- 5$ and simplify.

Divide each term in $- 5 Y = 10 - 2 X$ by $- 5$ .

$\frac{- 5 Y}{- 5} = \frac{10}{- 5} + \frac{- 2 X}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 Y}{- 5} = \frac{10}{- 5} + \frac{- 2 X}{- 5}$

Divide $Y$ by $1$ .

$Y = \frac{10}{- 5} + \frac{- 2 X}{- 5}$

Simplify the right side.

Simplify each term.

Divide $10$ by $- 5$ .

$Y = - 2 + \frac{- 2 X}{- 5}$

Dividing two negative values results in a positive value.

$Y = - 2 + \frac{2 X}{5}$

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

Rearrange terms.

$Y = \frac{2 X}{5} - 2$

Reorder terms.

$Y = \frac{2}{5} X - 2$

Step 2

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

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

$m = \frac{2}{5}$

$b = - 2$

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

Slope: $\frac{2}{5}$

y-intercept: $(0, - 2)$

Slope: $\frac{2}{5}$

y-intercept: $(0, - 2)$

Step 3