Algebra Examples

$(- 3, 16)$ , $(0, - 20)$

Step 1

Find the equation using the two points.

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Step 1.1

Use $y = m x + b$ to calculate the equation of the line, where $m$ represents the slope and $b$ represents the y-intercept.

To calculate the equation of the line, use the $y = m x + b$ format.

Step 1.2

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{(change in y)}{(change in x)}$

Step 1.3

The change in $x$ is equal to the difference in x-coordinates (also called run), and the change in $y$ is equal to the difference in y-coordinates (also called rise).

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Step 1.4

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{- 20 - (16)}{0 - (- 3)}$

Step 1.5

Finding the slope $m$ .

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Step 1.5.1

Simplify the numerator.

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Step 1.5.1.1

Multiply $- 1$ by $16$ .

$m = \frac{- 20 - 16}{0 - (- 3)}$

Step 1.5.1.2

Subtract $16$ from $- 20$ .

$m = \frac{- 36}{0 - (- 3)}$

Step 1.5.2

Simplify the denominator.

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Step 1.5.2.1

Multiply $- 1$ by $- 3$ .

$m = \frac{- 36}{0 + 3}$

Step 1.5.2.2

Add $0$ and $3$ .

$m = \frac{- 36}{3}$

Step 1.5.3

Divide $- 36$ by $3$ .

$m = - 12$

Step 1.6

Find the value of $b$ using the formula for the equation of a line.

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Step 1.6.1

Use the formula for the equation of a line to find $b$ .

$y = m x + b$

Step 1.6.2

Substitute the value of $m$ into the equation.

$y = (- 12) \cdot x + b$

Step 1.6.3

Substitute the value of $x$ into the equation.

$y = (- 12) \cdot (- 3) + b$

Step 1.6.4

Substitute the value of $y$ into the equation.

$16 = (- 12) \cdot (- 3) + b$

Step 1.6.5

Find the value of $b$ .

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Step 1.6.5.1

Rewrite the equation as $(- 12) \cdot (- 3) + b = 16$ .

$(- 12) \cdot (- 3) + b = 16$

Step 1.6.5.2

Multiply $- 12$ by $- 3$ .

$36 + b = 16$

Step 1.6.5.3

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

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Step 1.6.5.3.1

Subtract $36$ from both sides of the equation.

$b = 16 - 36$

Step 1.6.5.3.2

Subtract $36$ from $16$ .

$b = - 20$

Step 1.7

Now that the values of $m$ (slope) and $b$ (y-intercept) are known, substitute them into $y = m x + b$ to find the equation of the line.

$y = - 12 x - 20$

Step 2

Find the x-intercepts.

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Step 2.1

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

$0 = - 12 x - 20$

Step 2.2

Solve the equation.

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Step 2.2.1

Rewrite the equation as $- 12 x - 20 = 0$ .

$- 12 x - 20 = 0$

Step 2.2.2

Add $20$ to both sides of the equation.

$- 12 x = 20$

Step 2.2.3

Divide each term in $- 12 x = 20$ by $- 12$ and simplify.

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Step 2.2.3.1

Divide each term in $- 12 x = 20$ by $- 12$ .

$\frac{- 12 x}{- 12} = \frac{20}{- 12}$

Step 2.2.3.2

Simplify the left side.

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Step 2.2.3.2.1

Cancel the common factor of $- 12$ .

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Step 2.2.3.2.1.1

Cancel the common factor.

$\frac{- 12 x}{- 12} = \frac{20}{- 12}$

Step 2.2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{20}{- 12}$

Step 2.2.3.3

Simplify the right side.

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Step 2.2.3.3.1

Cancel the common factor of $20$ and $- 12$ .

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Step 2.2.3.3.1.1

Factor $4$ out of $20$ .

$x = \frac{4 (5)}{- 12}$

Step 2.2.3.3.1.2

Cancel the common factors.

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Step 2.2.3.3.1.2.1

Factor $4$ out of $- 12$ .

$x = \frac{4 \cdot 5}{4 \cdot - 3}$

Step 2.2.3.3.1.2.2

Cancel the common factor.

$x = \frac{4 \cdot 5}{4 \cdot - 3}$

Step 2.2.3.3.1.2.3

Rewrite the expression.

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

Step 2.2.3.3.2

Move the negative in front of the fraction.

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

Step 2.3

x-intercept(s) in point form.

x-intercept(s): $(- \frac{5}{3}, 0)$

Step 3

Find the y-intercepts.

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Step 3.1

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

$y = - 12 \cdot 0 - 20$

Step 3.2

Solve the equation.

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Step 3.2.1

Remove parentheses.

$y = - 12 \cdot 0 - 20$

Step 3.2.2

Simplify $- 12 \cdot 0 - 20$ .

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Step 3.2.2.1

Multiply $- 12$ by $0$ .

$y = 0 - 20$

Step 3.2.2.2

Subtract $20$ from $0$ .

$y = - 20$

Step 3.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 20)$

Step 4

List the intersections.

x-intercept(s): $(- \frac{5}{3}, 0)$

y-intercept(s): $(0, - 20)$

Step 5