Graph y=-3x+11 3y=5x-9

$y = - 3 x + 11$ $3 y = 5 x - 9$

Step 1

Graph $y = - 3 x + 11$ .

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

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

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

$m = - 3$

$b = 11$

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

Slope: $- 3$

y-intercept: $(0, 11)$

Slope: $- 3$

y-intercept: $(0, 11)$

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

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

$\begin{array}{c} x & y \\ 0 & 11 \\ 1 & 8 \end{array}$

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

Slope: $- 3$

y-intercept: $(0, 11)$

$\begin{array}{c} x & y \\ 0 & 11 \\ 1 & 8 \end{array}$

Slope: $- 3$

y-intercept: $(0, 11)$

$\begin{array}{c} x & y \\ 0 & 11 \\ 1 & 8 \end{array}$

Step 2

Graph $3 y = 5 x - 9$ .

Divide each term in $3 y = 5 x - 9$ by $3$ and simplify.

Divide each term in $3 y = 5 x - 9$ by $3$ .

$\frac{3 y}{3} = \frac{5 x}{3} + \frac{- 9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{5 x}{3} + \frac{- 9}{3}$

Divide $y$ by $1$ .

$y = \frac{5 x}{3} + \frac{- 9}{3}$

Simplify the right side.

Divide $- 9$ by $3$ .

$y = \frac{5 x}{3} - 3$

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.

$y = m x + b$

Reorder terms.

$y = \frac{5}{3} x - 3$

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

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

$m = \frac{5}{3}$

$b = - 3$

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

Slope: $\frac{5}{3}$

y-intercept: $(0, - 3)$

Slope: $\frac{5}{3}$

y-intercept: $(0, - 3)$

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

Reorder terms.

$y = \frac{5}{3} x - 3$

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

$\begin{array}{c} x & y \\ 0 & - 3 \\ 3 & 2 \end{array}$

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

Slope: $\frac{5}{3}$

y-intercept: $(0, - 3)$

$\begin{array}{c} x & y \\ 0 & - 3 \\ 3 & 2 \end{array}$

Slope: $\frac{5}{3}$

y-intercept: $(0, - 3)$

$\begin{array}{c} x & y \\ 0 & - 3 \\ 3 & 2 \end{array}$

Step 3

Plot each graph on the same coordinate system.

$y = - 3 x + 11$

$3 y = 5 x - 9$

Step 4

Graph y=-3x+11 3y=5x-9

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