Graph 4x+y=25

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Trigonometry

Graph 4x+y=25

$4 x + y = 25$

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

$y = 25 - 4 x$

Rewrite 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.

$y = m x + b$

Reorder $25$ and $- 4 x$ .

$y = - 4 x + 25$

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 $y = m x + b$ .

$m = - 4$

$b = 25$

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

Slope: $- 4$

y-intercept: $(0, 25)$

Slope: $- 4$

y-intercept: $(0, 25)$

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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Find the x-intercept.

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

$0 = 25 - 4 x$

Solve the equation.

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Rewrite the equation as $25 - 4 x = 0$ .

$25 - 4 x = 0$

Subtract $25$ from both sides of the equation.

$- 4 x = - 25$

Divide each term by $- 4$ and simplify.

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Divide each term in $- 4 x = - 25$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 25}{- 4}$

Cancel the common factor of $- 4$ .

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Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 25}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- 25}{- 4}$

Dividing two negative values results in a positive value.

$x = \frac{25}{4}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{25}{4}, 0)$

Find the y-intercept.

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

$y = 25 - 4 \cdot 0$

Solve the equation.

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Remove parentheses.

$y = 25 - 4 \cdot 0$

Simplify $25 - 4 \cdot 0$ .

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Multiply $- 4$ by $0$ .

$y = 25 + 0$

Add $25$ and $0$ .

$y = 25$

y-intercept(s) in point form.

y-intercept(s): $(0, 25)$

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

$\begin{array}{c} x & y \\ 0 & 25 \\ \frac{25}{4} & 0 \end{array}$

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

Slope: $- 4$

y-intercept: $(0, 25)$

$\begin{array}{c} x & y \\ 0 & 25 \\ \frac{25}{4} & 0 \end{array}$

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