Graph three x plus four y equals twelve

$3 x + 4 y = 12$

Calculate $y$ .

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Subtract $3 x$ from both sides of the equation.

$4 y = 12 - 3 x$

First, divide each term by $4$ and Clarify.

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Divide each term in $4 y = 12 - 3 x$ by $4$ .

$\frac{4 y}{4} = \frac{12}{4} + \frac{- 3 x}{4}$

The common factor should be canceled of $4$ .

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Cancel the common factor.

$\frac{4 y}{4} = \frac{12}{4} + \frac{- 3 x}{4}$

Divide $y$ by $1$ .

$y = \frac{12}{4} + \frac{- 3 x}{4}$

Clarify each term.

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Divide $12$ by $4$ .

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

Put the negative in front of the fraction.

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

Should be rewritten in slope-intercept form.

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

$y = m x + b$

Shift $3$ and $- \frac{3 x}{4}$ .

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

Rewrite in slope-intercept form.

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

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

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

$m = - \frac{3}{4}$

$b = 3$

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

Slope: $- \frac{3}{4}$

y-intercept: $3$

Slope: $- \frac{3}{4}$

y-intercept: $3$

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

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Choose $0$ to substitute in for $x$ to find the ordered pair.

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Replace the variable $x$ with $0$ in the expression.

$f (0) = - \frac{3 (0)}{4} + 3$

Clarify the result.

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Simplify each term.

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The common factor $0$ should be canceled and $4$ .

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Factor $4$ out of $3 (0)$ .

$f (0) = - \frac{4 (3 \cdot (0))}{4} + 3$

The common factors should be canceled.

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Factor $4$ out of $4$ .

$f (0) = - \frac{4 (3 \cdot (0))}{4 (1)} + 3$

Cancel the common factor.

$f (0) = - \frac{4 (3 \cdot (0))}{4 \cdot 1} + 3$

Reformulate the expression.

$f (0) = - \frac{3 \cdot (0)}{1} + 3$

Divide $3 \cdot (0)$ by $1$ .

$f (0) = - (3 \cdot (0)) + 3$

First, multiply $3$ by $0$ .

$f (0) = - 0 + 3$

Multiply $- 1$ by $0$ .

$f (0) = 0 + 3$

Sum $0$ and $3$ .

$f (0) = 3$

The result is $3$ .

$3$

The $y$ value at $x = 0$ is $3$ .

$y = 3$

Choose $1$ to substitute in for $x$ to find the ordered pair.

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Replace the variable $x$ with $1$ in the expression.

$f (1) = - \frac{3 (1)}{4} + 3$

Simplify the result.

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Multiply $3$ by $1$ .

$f (1) = - \frac{3}{4} + 3$

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$f (1) = - \frac{3}{4} + 3 \cdot \frac{4}{4}$

Add $3$ and $\frac{4}{4}$ .

$f (1) = - \frac{3}{4} + \frac{3 \cdot 4}{4}$

Add numerators over the common denominator.

$f (1) = \frac{- 3 + 3 \cdot 4}{4}$

Clarify the numerator.

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Multiply $3$ by $4$ .

$f (1) = \frac{- 3 + 12}{4}$

Add $- 3$ and $12$ .

$f (1) = \frac{9}{4}$

The final answer is $\frac{9}{4}$ .

$\frac{9}{4}$

The $y$ value at $x = 1$ is $\frac{9}{4}$ .

$y = \frac{9}{4}$

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

$\begin{array}{c} x & y \\ 0 & 3 \\ 1 & \frac{9}{4} \end{array}$

Plot the line with the slope and the y-intercept, or the points.

Slope: $- \frac{3}{4}$

y-intercept: $3$

$\begin{array}{c} x & y \\ 0 & 3 \\ 1 & \frac{9}{4} \end{array}$

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