Calculus Examples

$y - 3 = - \frac{1}{13} \cdot (x - 1)$

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 $x$ .

$(0) - 3 = - \frac{1}{13} \cdot (x - 1)$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $- \frac{1}{13} \cdot (x - 1) = (0) - 3$ .

$- \frac{1}{13} \cdot (x - 1) = (0) - 3$

Step 1.2.2

Multiply both sides of the equation by $- 13$ .

$- 13 (- \frac{1}{13} \cdot (x - 1)) = - 13 ((0) - 3)$

Step 1.2.3

Simplify both sides of the equation.

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Step 1.2.3.1

Simplify the left side.

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Step 1.2.3.1.1

Simplify $- 13 (- \frac{1}{13} \cdot (x - 1))$ .

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Step 1.2.3.1.1.1

Apply the distributive property.

$- 13 (- \frac{1}{13} x - \frac{1}{13} \cdot - 1) = - 13 ((0) - 3)$

Step 1.2.3.1.1.2

Combine $x$ and $\frac{1}{13}$ .

$- 13 (- \frac{x}{13} - \frac{1}{13} \cdot - 1) = - 13 ((0) - 3)$

Step 1.2.3.1.1.3

Multiply $- \frac{1}{13} \cdot - 1$ .

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Step 1.2.3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$- 13 (- \frac{x}{13} + 1 (\frac{1}{13})) = - 13 ((0) - 3)$

Step 1.2.3.1.1.3.2

Multiply $\frac{1}{13}$ by $1$ .

$- 13 (- \frac{x}{13} + \frac{1}{13}) = - 13 ((0) - 3)$

Step 1.2.3.1.1.4

Apply the distributive property.

$- 13 (- \frac{x}{13}) - 13 (\frac{1}{13}) = - 13 ((0) - 3)$

Step 1.2.3.1.1.5

Cancel the common factor of $13$ .

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Step 1.2.3.1.1.5.1

Move the leading negative in $- \frac{x}{13}$ into the numerator.

$- 13 \frac{- x}{13} - 13 (\frac{1}{13}) = - 13 ((0) - 3)$

Step 1.2.3.1.1.5.2

Factor $13$ out of $- 13$ .

$13 (- 1) \frac{- x}{13} - 13 (\frac{1}{13}) = - 13 ((0) - 3)$

Step 1.2.3.1.1.5.3

Cancel the common factor.

$13 \cdot - 1 \frac{- x}{13} - 13 (\frac{1}{13}) = - 13 ((0) - 3)$

Step 1.2.3.1.1.5.4

Rewrite the expression.

$- - x - 13 (\frac{1}{13}) = - 13 ((0) - 3)$

Step 1.2.3.1.1.6

Multiply.

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Step 1.2.3.1.1.6.1

Multiply $- 1$ by $- 1$ .

$1 x - 13 (\frac{1}{13}) = - 13 ((0) - 3)$

Step 1.2.3.1.1.6.2

Multiply $x$ by $1$ .

$x - 13 (\frac{1}{13}) = - 13 ((0) - 3)$

Step 1.2.3.1.1.7

Cancel the common factor of $13$ .

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Step 1.2.3.1.1.7.1

Factor $13$ out of $- 13$ .

$x + 13 (- 1) \frac{1}{13} = - 13 ((0) - 3)$

Step 1.2.3.1.1.7.2

Cancel the common factor.

$x + 13 \cdot - 1 \frac{1}{13} = - 13 ((0) - 3)$

Step 1.2.3.1.1.7.3

Rewrite the expression.

$x - 1 = - 13 ((0) - 3)$

Step 1.2.3.2

Simplify the right side.

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Step 1.2.3.2.1

Simplify $- 13 ((0) - 3)$ .

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Step 1.2.3.2.1.1

Subtract $3$ from $0$ .

$x - 1 = - 13 \cdot - 3$

Step 1.2.3.2.1.2

Multiply $- 13$ by $- 3$ .

$x - 1 = 39$

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

Add $1$ to both sides of the equation.

$x = 39 + 1$

Step 1.2.4.2

Add $39$ and $1$ .

$x = 40$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(40, 0)$

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 $y$ .

$y - 3 = - \frac{1}{13} \cdot ((0) - 1)$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $- \frac{1}{13} \cdot ((0) - 1)$ .

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Step 2.2.1.1

Subtract $1$ from $0$ .

$y - 3 = - \frac{1}{13} \cdot - 1$

Step 2.2.1.2

Multiply $- \frac{1}{13} \cdot - 1$ .

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Step 2.2.1.2.1

Multiply $- 1$ by $- 1$ .

$y - 3 = 1 (\frac{1}{13})$

Step 2.2.1.2.2

Multiply $\frac{1}{13}$ by $1$ .

$y - 3 = \frac{1}{13}$

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 $3$ to both sides of the equation.

$y = \frac{1}{13} + 3$

Step 2.2.2.2

To write $3$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$y = \frac{1}{13} + 3 \cdot \frac{13}{13}$

Step 2.2.2.3

Combine $3$ and $\frac{13}{13}$ .

$y = \frac{1}{13} + \frac{3 \cdot 13}{13}$

Step 2.2.2.4

Combine the numerators over the common denominator.

$y = \frac{1 + 3 \cdot 13}{13}$

Step 2.2.2.5

Simplify the numerator.

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Step 2.2.2.5.1

Multiply $3$ by $13$ .

$y = \frac{1 + 39}{13}$

Step 2.2.2.5.2

Add $1$ and $39$ .

$y = \frac{40}{13}$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{40}{13})$

Step 3

List the intersections.

x-intercept(s): $(40, 0)$

y-intercept(s): $(0, \frac{40}{13})$

Step 4