Graph 8x-2(x-7)

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Trigonometry

Graph 8x-2(x-7)

$8 x - 2 (x - 7)$

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

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

$y = m x + b$

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

$m = 6$

$b = 14$

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

Slope: $6$

y-intercept: $(0, 14)$

Slope: $6$

y-intercept: $(0, 14)$

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 $x$ .

$0 = 6 x + 14$

Solve the equation.

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Rewrite the equation as $6 x + 14 = 0$ .

$6 x + 14 = 0$

Subtract $14$ from both sides of the equation.

$6 x = - 14$

Divide each term by $6$ and simplify.

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Divide each term in $6 x = - 14$ by $6$ .

$\frac{6 x}{6} = \frac{- 14}{6}$

Cancel the common factor of $6$ .

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Cancel the common factor.

$\frac{6 x}{6} = \frac{- 14}{6}$

Divide $x$ by $1$ .

$x = \frac{- 14}{6}$

Simplify $\frac{- 14}{6}$ .

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Cancel the common factor of $- 14$ and $6$ .

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Factor $2$ out of $- 14$ .

$x = \frac{2 (- 7)}{6}$

Cancel the common factors.

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Factor $2$ out of $6$ .

$x = \frac{2 \cdot - 7}{2 \cdot 3}$

Cancel the common factor.

$x = \frac{2 \cdot - 7}{2 \cdot 3}$

Rewrite the expression.

$x = \frac{- 7}{3}$

Move the negative in front of the fraction.

$x = - \frac{7}{3}$

x-intercept(s) in point form.

x-intercept(s): $(- \frac{7}{3}, 0)$

Find the y-intercept.

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

$y = 6 (0) + 14$

Solve the equation.

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Remove parentheses.

$y = 6 (0) + 14$

Simplify $6 (0) + 14$ .

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Multiply $6$ by $0$ .

$y = 0 + 14$

Add $0$ and $14$ .

$y = 14$

y-intercept(s) in point form.

y-intercept(s): $(0, 14)$

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

$\begin{array}{c} x & y \\ - \frac{7}{3} & 0 \\ 0 & 14 \end{array}$

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

Slope: $6$

y-intercept: $(0, 14)$

$\begin{array}{c} x & y \\ - \frac{7}{3} & 0 \\ 0 & 14 \end{array}$

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