Algebra Examples

$y - 6 = 4 (x + 5)$

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 $x$ .

$(0) - 6 = 4 (x + 5)$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $4 (x + 5) = (0) - 6$ .

$4 (x + 5) = (0) - 6$

Step 1.2.2

Subtract $6$ from $0$ .

$4 (x + 5) = - 6$

Step 1.2.3

Divide each term in $4 (x + 5) = - 6$ by $4$ and simplify.

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Step 1.2.3.1

Divide each term in $4 (x + 5) = - 6$ by $4$ .

$\frac{4 (x + 5)}{4} = \frac{- 6}{4}$

Step 1.2.3.2

Simplify the left side.

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Step 1.2.3.2.1

Cancel the common factor of $4$ .

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Step 1.2.3.2.1.1

Cancel the common factor.

$\frac{4 (x + 5)}{4} = \frac{- 6}{4}$

Step 1.2.3.2.1.2

Divide $x + 5$ by $1$ .

$x + 5 = \frac{- 6}{4}$

Step 1.2.3.3

Simplify the right side.

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Step 1.2.3.3.1

Cancel the common factor of $- 6$ and $4$ .

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Step 1.2.3.3.1.1

Factor $2$ out of $- 6$ .

$x + 5 = \frac{2 (- 3)}{4}$

Step 1.2.3.3.1.2

Cancel the common factors.

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Step 1.2.3.3.1.2.1

Factor $2$ out of $4$ .

$x + 5 = \frac{2 \cdot - 3}{2 \cdot 2}$

Step 1.2.3.3.1.2.2

Cancel the common factor.

$x + 5 = \frac{2 \cdot - 3}{2 \cdot 2}$

Step 1.2.3.3.1.2.3

Rewrite the expression.

$x + 5 = \frac{- 3}{2}$

Step 1.2.3.3.2

Move the negative in front of the fraction.

$x + 5 = - \frac{3}{2}$

Step 1.2.4

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

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Step 1.2.4.1

Subtract $5$ from both sides of the equation.

$x = - \frac{3}{2} - 5$

Step 1.2.4.2

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = - \frac{3}{2} - 5 \cdot \frac{2}{2}$

Step 1.2.4.3

Combine $- 5$ and $\frac{2}{2}$ .

$x = - \frac{3}{2} + \frac{- 5 \cdot 2}{2}$

Step 1.2.4.4

Combine the numerators over the common denominator.

$x = \frac{- 3 - 5 \cdot 2}{2}$

Step 1.2.4.5

Simplify the numerator.

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Step 1.2.4.5.1

Multiply $- 5$ by $2$ .

$x = \frac{- 3 - 10}{2}$

Step 1.2.4.5.2

Subtract $10$ from $- 3$ .

$x = \frac{- 13}{2}$

Step 1.2.4.6

Move the negative in front of the fraction.

$x = - \frac{13}{2}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- \frac{13}{2}, 0)$

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 $y$ .

$y - 6 = 4 ((0) + 5)$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $4 ((0) + 5)$ .

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Step 2.2.1.1

Add $0$ and $5$ .

$y - 6 = 4 \cdot 5$

Step 2.2.1.2

Multiply $4$ by $5$ .

$y - 6 = 20$

Step 2.2.2

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

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Step 2.2.2.1

Add $6$ to both sides of the equation.

$y = 20 + 6$

Step 2.2.2.2

Add $20$ and $6$ .

$y = 26$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 26)$

Step 3

List the intersections.

x-intercept(s): $(- \frac{13}{2}, 0)$

y-intercept(s): $(0, 26)$

Step 4