Graph y=-3x+11 2y=4x-5

$y = - 3 x + 11$ $2 y = 4 x - 5$

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 $2 y = 4 x - 5$ .

Divide each term in $2 y = 4 x - 5$ by $2$ and simplify.

Divide each term in $2 y = 4 x - 5$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 x$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

$y = \frac{2 (2 x)}{2 (1)} + \frac{- 5}{2}$

Cancel the common factor.

$y = \frac{2 (2 x)}{2 \cdot 1} + \frac{- 5}{2}$

Rewrite the expression.

$y = \frac{2 x}{1} + \frac{- 5}{2}$

Divide $2 x$ by $1$ .

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

Move the negative in front of the fraction.

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

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 $y = m x + b$ .

$m = 2$

$b = - \frac{5}{2}$

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

Slope: $2$

y-intercept: $(0, - \frac{5}{2})$

Slope: $2$

y-intercept: $(0, - \frac{5}{2})$

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

Find the x-intercept.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = 2 x - \frac{5}{2}$

Solve the equation.

Rewrite the equation as $2 x - \frac{5}{2} = 0$ .

$2 x - \frac{5}{2} = 0$

Add $\frac{5}{2}$ to both sides of the equation.

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

Divide each term in $2 x = \frac{5}{2}$ by $2$ and simplify.

Divide each term in $2 x = \frac{5}{2}$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{5}{2} \cdot \frac{1}{2}$

Multiply $\frac{5}{2} \cdot \frac{1}{2}$ .

Multiply $\frac{5}{2}$ by $\frac{1}{2}$ .

$x = \frac{5}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{5}{4}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{5}{4}, 0)$

Find the y-intercept.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = 2 (0) - \frac{5}{2}$

Solve the equation.

Remove parentheses.

$y = 2 (0) - \frac{5}{2}$

Simplify $2 (0) - \frac{5}{2}$ .

Multiply $2$ by $0$ .

$y = 0 - \frac{5}{2}$

Subtract $\frac{5}{2}$ from $0$ .

$y = - \frac{5}{2}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{5}{2})$

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

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

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

Slope: $2$

y-intercept: $(0, - \frac{5}{2})$

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

Slope: $2$

y-intercept: $(0, - \frac{5}{2})$

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

Step 3

Plot each graph on the same coordinate system.

$y = - 3 x + 11$

$2 y = 4 x - 5$

Step 4

Graph y=-3x+11 2y=4x-5

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