Graph 4x-10y=-20 6x-15y=-30

$4 x - 10 y = - 20$ $6 x - 15 y = - 30$

Graph $4 x - 10 y = - 20$ .

Solve for $y$ .

Subtract $4 x$ from both sides of the equation.

$- 10 y = - 20 - 4 x$

Divide each term in $- 10 y = - 20 - 4 x$ by $- 10$ and simplify.

Divide each term in $- 10 y = - 20 - 4 x$ by $- 10$ .

$\frac{- 10 y}{- 10} = \frac{- 20}{- 10} + \frac{- 4 x}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 y}{- 10} = \frac{- 20}{- 10} + \frac{- 4 x}{- 10}$

Divide $y$ by $1$ .

$y = \frac{- 20}{- 10} + \frac{- 4 x}{- 10}$

Simplify the right side.

Simplify each term.

Divide $- 20$ by $- 10$ .

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

Cancel the common factor of $- 4$ and $- 10$ .

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

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

Cancel the common factors.

Factor $- 2$ out of $- 10$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y = 2 + \frac{2 x}{5}$

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.

$y = m x + b$

Reorder $2$ and $\frac{2 x}{5}$ .

$y = \frac{2 x}{5} + 2$

Reorder terms.

$y = \frac{2}{5} x + 2$

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: $(0, 2)$

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

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

Reorder $2$ and $\frac{2 x}{5}$ .

$y = \frac{2 x}{5} + 2$

Reorder terms.

$y = \frac{2}{5} x + 2$

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & 2 \\ 5 & 4 \end{array}$

Graph the line using the slope and the y-intercept, or the points.

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

y-intercept: $(0, 2)$

$\begin{array}{c} x & y \\ 0 & 2 \\ 5 & 4 \end{array}$

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

y-intercept: $(0, 2)$

$\begin{array}{c} x & y \\ 0 & 2 \\ 5 & 4 \end{array}$

Plot each graph on the same coordinate system.

$4 x - 10 y = - 20$

$6 x - 15 y = - 30$

Graph 4x-10y=-20 6x-15y=-30

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