Graph x plus two y equals four

$x + 2 y = 4$

Calculate $y$ .

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Subtract $x$ from both sides of the equation.

$2 y = 4 - x$

First, divide each term by $2$ and Clarify.

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

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

The common factor should be canceled of $2$ .

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Cancel the common factor.

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

Divide $y$ by $1$ .

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

Clarify each term.

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Divide $4$ by $2$ .

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

Put the negative in front of the fraction.

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

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 $2$ and $- \frac{x}{2}$ .

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

Rewrite in slope-intercept form.

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

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 $y = m x + b$ .

$m = - \frac{1}{2}$

$b = 2$

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

Slope: $- \frac{1}{2}$

y-intercept: $2$

Slope: $- \frac{1}{2}$

y-intercept: $2$

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

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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.

$f (0) = - \frac{0}{2} + 2$

Clarify the result.

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Simplify each term.

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Initially, divide $0$ by $2$ .

$f (0) = - 0 + 2$

First, multiply $- 1$ by $0$ .

$f (0) = 0 + 2$

Sum $0$ and $2$ .

$f (0) = 2$

The result is $2$ .

$2$

The $y$ value at $x = 0$ is $2$ .

$y = 2$

Choose $2$ to substitute in for $x$ to find the ordered pair.

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Replace the variable $x$ with $2$ in the expression.

$f (2) = - \frac{2}{2} + 2$

Simplify the result.

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Simplify each term.

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Divide $2$ by $2$ .

$f (2) = - 1 \cdot 1 + 2$

Multiply $- 1$ by $1$ .

$f (2) = - 1 + 2$

Add $- 1$ and $2$ .

$f (2) = 1$

The result is $1$ .

$1$

The $y$ value at $x = 2$ is $1$ .

$y = 1$

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

$\begin{array}{c} x & y \\ 0 & 2 \\ 2 & 1 \end{array}$

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

Slope: $- \frac{1}{2}$

y-intercept: $2$

$\begin{array}{c} x & y \\ 0 & 2 \\ 2 & 1 \end{array}$

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