Graph y=3/4x-7/2

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Trigonometry

Graph y=3/4x-7/2

$y = \frac{3}{4} x - \frac{7}{2}$

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 terms.

$y = \frac{3}{4} x - \frac{7}{2}$

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 $y = m x + b$ .

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

$b = - \frac{7}{2}$

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

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

y-intercept: $(0, - \frac{7}{2})$

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

y-intercept: $(0, - \frac{7}{2})$

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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Find the x-intercept.

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

$0 = \frac{3 x}{4} - \frac{7}{2}$

Solve the equation.

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Rewrite the equation as $\frac{3 x}{4} - \frac{7}{2} = 0$ .

$\frac{3 x}{4} - \frac{7}{2} = 0$

Add $\frac{7}{2}$ to both sides of the equation.

$\frac{3 x}{4} = \frac{7}{2}$

Multiply both sides of the equation by $\frac{4}{3}$ .

$\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} \cdot \frac{7}{2}$

Simplify both sides of the equation.

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Simplify $\frac{4}{3} \cdot \frac{3 x}{4}$ .

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Cancel the common factor of $4$ .

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Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} \cdot \frac{7}{2}$

Rewrite the expression.

$\frac{1}{3} \cdot (3 x) = \frac{4}{3} \cdot \frac{7}{2}$

Cancel the common factor of $3$ .

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Factor $3$ out of $3 x$ .

$\frac{1}{3} \cdot (3 (x)) = \frac{4}{3} \cdot \frac{7}{2}$

Cancel the common factor.

$\frac{1}{3} \cdot (3 x) = \frac{4}{3} \cdot \frac{7}{2}$

Rewrite the expression.

$x = \frac{4}{3} \cdot \frac{7}{2}$

Simplify $\frac{4}{3} \cdot \frac{7}{2}$ .

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Cancel the common factor of $2$ .

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Factor $2$ out of $4$ .

$x = \frac{2 (2)}{3} \cdot \frac{7}{2}$

Cancel the common factor.

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

Rewrite the expression.

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

Combine $\frac{2}{3}$ and $7$ .

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

Multiply $2$ by $7$ .

$x = \frac{14}{3}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{14}{3}, 0)$

Find the y-intercept.

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

$y = \frac{3 (0)}{4} - \frac{7}{2}$

Solve the equation.

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Remove parentheses.

$y = \frac{3 (0)}{4} - \frac{7}{2}$

Simplify $\frac{3 (0)}{4} - \frac{7}{2}$ .

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Multiply $3$ by $0$ .

$y = \frac{0}{4} - \frac{7}{2}$

Divide $0$ by $4$ .

$y = 0 - \frac{7}{2}$

Subtract $\frac{7}{2}$ from $0$ .

$y = - \frac{7}{2}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{7}{2})$

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

$\begin{array}{c} x & y \\ 0 & - \frac{7}{2} \\ \frac{14}{3} & 0 \end{array}$

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

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

y-intercept: $(0, - \frac{7}{2})$

$\begin{array}{c} x & y \\ 0 & - \frac{7}{2} \\ \frac{14}{3} & 0 \end{array}$

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