Pre-Algebra Examples

(- 5, 0)

$(- 5, 0)$ ,

(0, 7)

$(0, 7)$

Step 1

Find the value of the slope.

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Step 1.1

Slope is equal to the change in

y

$y$ over the change in

x

$x$ , or rise over run.

m = \frac{change in y}{change in x}

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

Step 1.2

The change in

x

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

y

$y$ is equal to the difference in y-coordinates (also called rise).

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

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

Step 1.3

Substitute in the values of

x

$x$ and

y

$y$ into the equation to find the slope.

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

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

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

$- 1$ by

0

$0$ .

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

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

Step 1.4.1.2

Add

7

$7$ and

0

$0$ .

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

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

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

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

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply

- 1

$- 1$ by

- 5

$- 5$ .

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

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

Step 1.4.2.2

Add

0

$0$ and

5

$5$ .

m = \frac{7}{5}

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

m = \frac{7}{5}

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

m = \frac{7}{5}

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

m = \frac{7}{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

$m$ into the slope-intercept form of the equation,

y = m x + b

$y = m x + b$ .

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

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

Step 2.2

Substitute the value of

x

$x$ into the slope-intercept form of the equation,

y = m x + b

$y = m x + b$ .

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

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

Step 2.3

Substitute the value of

y

$y$ into the slope-intercept form of the equation,

y = m x + b

$y = m x + b$ .

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

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

Step 2.4

Rewrite the equation as

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

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

(\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

$5$ .

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Step 2.5.1.1

Factor

5

$5$ out of

- 5

$- 5$ .

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

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

Step 2.5.1.2

Cancel the common factor.

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

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

Step 2.5.1.3

Rewrite the expression.

7 \cdot - 1 + b = 0

$7 \cdot - 1 + b = 0$

7 \cdot - 1 + b = 0

$7 \cdot - 1 + b = 0$

Step 2.5.2

Multiply

7

$7$ by

- 1

$- 1$ .

- 7 + b = 0

$- 7 + b = 0$

- 7 + b = 0

$- 7 + b = 0$

Step 2.6

Add

7

$7$ to both sides of the equation.

b = 7

$b = 7$

b = 7

$b = 7$

Step 3

List the slope and y-intercept.

Slope:

\frac{7}{5}

$\frac{7}{5}$

y-intercept:

(0, 7)

$(0, 7)$

Step 4