Pre-Algebra Examples

$(- \frac{1}{2}, 0)$ , $(0, 1)$

Step 1

Find the value of the slope.

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Step 1.1

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 1.2

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 1.3

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

$m = \frac{1 - (0)}{0 - (- \frac{1}{2})}$

Step 1.4

Simplify.

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Step 1.4.1

Simplify the numerator.

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Step 1.4.1.1

Multiply $- 1$ by $0$ .

$m = \frac{1 + 0}{0 + \frac{1}{2}}$

Step 1.4.1.2

Add $1$ and $0$ .

$m = \frac{1}{0 + \frac{1}{2}}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- - \frac{1}{2}$ .

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Step 1.4.2.1.1

Multiply $- 1$ by $- 1$ .

$m = \frac{1}{0 + 1 (\frac{1}{2})}$

Step 1.4.2.1.2

Multiply $\frac{1}{2}$ by $1$ .

$m = \frac{1}{0 + \frac{1}{2}}$

Step 1.4.2.2

Add $0$ and $\frac{1}{2}$ .

$m = \frac{1}{\frac{1}{2}}$

Step 1.4.3

Multiply the numerator by the reciprocal of the denominator.

$m = 1 \cdot 2$

Step 1.4.4

Multiply $2$ by $1$ .

$m = 2$

Step 2

Find the value of the y-intercept.

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Step 2.1

Substitute the value of $m$ into the slope-intercept form of the equation, $y = m x + b$ .

$y = (2) \cdot x + b$

Step 2.2

Substitute the value of $x$ into the slope-intercept form of the equation, $y = m x + b$ .

$y = (2) \cdot (- \frac{1}{2}) + b$

Step 2.3

Substitute the value of $y$ into the slope-intercept form of the equation, $y = m x + b$ .

$0 = (2) \cdot (- \frac{1}{2}) + b$

Step 2.4

Rewrite the equation as $(2) \cdot (- \frac{1}{2}) + b = 0$ .

$(2) \cdot (- \frac{1}{2}) + b = 0$

Step 2.5

Cancel the common factor of $2$ .

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Step 2.5.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$2 \cdot \frac{- 1}{2} + b = 0$

Step 2.5.2

Cancel the common factor.

$2 \cdot \frac{- 1}{2} + b = 0$

Step 2.5.3

Rewrite the expression.

$- 1 + b = 0$

Step 2.6

Add $1$ to both sides of the equation.

$b = 1$

Step 3

List the slope and y-intercept.

Slope: $2$

y-intercept: $(0, 1)$

Step 4