Precalculus Examples

$8 x + 5 = 8 y + 5$

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 $x$ .

$8 x + 5 = 8 (0) + 5$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify $8 (0) + 5$ .

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Step 1.2.1.1

Multiply $8$ by $0$ .

$8 x + 5 = 0 + 5$

Step 1.2.1.2

Add $0$ and $5$ .

$8 x + 5 = 5$

Step 1.2.2

Move all terms not containing $x$ to the right side of the equation.

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Step 1.2.2.1

Subtract $5$ from both sides of the equation.

$8 x = 5 - 5$

Step 1.2.2.2

Subtract $5$ from $5$ .

$8 x = 0$

Step 1.2.3

Divide each term in $8 x = 0$ by $8$ and simplify.

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Step 1.2.3.1

Divide each term in $8 x = 0$ by $8$ .

$\frac{8 x}{8} = \frac{0}{8}$

Step 1.2.3.2

Simplify the left side.

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Step 1.2.3.2.1

Cancel the common factor of $8$ .

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Step 1.2.3.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{0}{8}$

Step 1.2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{8}$

Step 1.2.3.3

Simplify the right side.

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Step 1.2.3.3.1

Divide $0$ by $8$ .

$x = 0$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(0, 0)$

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 $y$ .

$8 (0) + 5 = 8 y + 5$

Step 2.2

Solve the equation.

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Step 2.2.1

Rewrite the equation as $8 y + 5 = 8 (0) + 5$ .

$8 y + 5 = 8 (0) + 5$

Step 2.2.2

Simplify $8 (0) + 5$ .

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Step 2.2.2.1

Multiply $8$ by $0$ .

$8 y + 5 = 0 + 5$

Step 2.2.2.2

Add $0$ and $5$ .

$8 y + 5 = 5$

Step 2.2.3

Move all terms not containing $y$ to the right side of the equation.

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Step 2.2.3.1

Subtract $5$ from both sides of the equation.

$8 y = 5 - 5$

Step 2.2.3.2

Subtract $5$ from $5$ .

$8 y = 0$

Step 2.2.4

Divide each term in $8 y = 0$ by $8$ and simplify.

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Step 2.2.4.1

Divide each term in $8 y = 0$ by $8$ .

$\frac{8 y}{8} = \frac{0}{8}$

Step 2.2.4.2

Simplify the left side.

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Step 2.2.4.2.1

Cancel the common factor of $8$ .

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Step 2.2.4.2.1.1

Cancel the common factor.

$\frac{8 y}{8} = \frac{0}{8}$

Step 2.2.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{0}{8}$

Step 2.2.4.3

Simplify the right side.

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Step 2.2.4.3.1

Divide $0$ by $8$ .

$y = 0$

Step 2.3

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(0, 0)$

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

Step 4