Pre-Algebra Examples

$(- 5, 0)$ , $(0, 7)$

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.

$m = \frac{7 - (0)}{0 - (- 5)}$

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 $0$ .

$m = \frac{7 + 0}{0 - (- 5)}$

Step 1.4.1.2

Add $7$ and $0$ .

$m = \frac{7}{0 - (- 5)}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $- 5$ .

$m = \frac{7}{0 + 5}$

Step 1.4.2.2

Add $0$ and $5$ .

$m = \frac{7}{5}$

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, $y = m x + b$ .

$y = (\frac{7}{5}) x + b$

Step 2.2

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

$y = (\frac{7}{5}) \cdot (- 5) + b$

Step 2.3

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

$0 = (\frac{7}{5}) \cdot (- 5) + b$

Step 2.4

Rewrite the equation as $(\frac{7}{5}) \cdot (- 5) + b = 0$ .

$(\frac{7}{5}) \cdot (- 5) + b = 0$

Step 2.5

Simplify each term.

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Step 2.5.1

Cancel the common factor of $5$ .

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Step 2.5.1.1

Factor $5$ out of $- 5$ .

$\frac{7}{5} \cdot (5 (- 1)) + b = 0$

Step 2.5.1.2

Cancel the common factor.

$\frac{7}{5} \cdot (5 \cdot - 1) + b = 0$

Step 2.5.1.3

Rewrite the expression.

$7 \cdot - 1 + b = 0$

Step 2.5.2

Multiply $7$ by $- 1$ .

$- 7 + b = 0$

Step 2.6

Add $7$ to both sides of the equation.

$b = 7$

Step 3

List the slope and y-intercept.

Slope: $\frac{7}{5}$

y-intercept: $(0, 7)$

Step 4