Algebra Examples

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

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in

$0$ for

$y$ and solve for

$x$ .

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

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as

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

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

Step 1.2.2

Combine

$\frac{2}{3}$ and

$x$ .

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

Step 1.2.3

Add

$4$ to both sides of the equation.

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

Step 1.2.4

Multiply both sides of the equation by

$\frac{3}{2}$ .

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

Step 1.2.5

Simplify both sides of the equation.

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Step 1.2.5.1

Simplify the left side.

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Step 1.2.5.1.1

Simplify

$\frac{3}{2} \cdot \frac{2 x}{3}$ .

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Step 1.2.5.1.1.1

Cancel the common factor of

$3$ .

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Step 1.2.5.1.1.1.1

Cancel the common factor.

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

Step 1.2.5.1.1.1.2

Rewrite the expression.

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

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

Step 1.2.5.1.1.2

Cancel the common factor of

$2$ .

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Step 1.2.5.1.1.2.1

Factor

$2$ out of

$2 x$ .

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

Step 1.2.5.1.1.2.2

Cancel the common factor.

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

Step 1.2.5.1.1.2.3

Rewrite the expression.

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

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

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

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

Step 1.2.5.2

Simplify the right side.

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Step 1.2.5.2.1

Simplify

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

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Step 1.2.5.2.1.1

Cancel the common factor of

$2$ .

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Step 1.2.5.2.1.1.1

Factor

$2$ out of

$4$ .

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

Step 1.2.5.2.1.1.2

Cancel the common factor.

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

Step 1.2.5.2.1.1.3

Rewrite the expression.

$x = 3 \cdot 2$

$x = 3 \cdot 2$

Step 1.2.5.2.1.2

Multiply

$3$ by

$2$ .

$x = 6$

$x = 6$

$x = 6$

$x = 6$

$x = 6$

Step 1.3

x-intercept(s) in point form.

x-intercept(s):

$(6, 0)$

x-intercept(s):

$(6, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in

$0$ for

$x$ and solve for

$y$ .

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

Step 2.2

Solve the equation.

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Step 2.2.1

Multiply

$\frac{2}{3}$ by

$0$ .

$y = \frac{2}{3} \cdot 0 - 4$

Step 2.2.2

Remove parentheses.

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

Step 2.2.3

Simplify

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

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Step 2.2.3.1

Multiply

$\frac{2}{3}$ by

$0$ .

$y = 0 - 4$

Step 2.2.3.2

Subtract

$4$ from

$0$ .

$y = - 4$

$y = - 4$

$y = - 4$

Step 2.3

y-intercept(s) in point form.

y-intercept(s):

$(0, - 4)$

y-intercept(s):

$(0, - 4)$

Step 3

List the intersections.

x-intercept(s):

$(6, 0)$

y-intercept(s):

$(0, - 4)$

Step 4

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$