Pre-Algebra Examples

(9, 4)

$(9, 4)$ ,

(4, 9)

$(4, 9)$

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{9 - (4)}{4 - (9)}

$m = \frac{9 - (4)}{4 - (9)}$

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

4

$4$ .

m = \frac{9 - 4}{4 - (9)}

$m = \frac{9 - 4}{4 - (9)}$

Step 1.4.1.2

Subtract

4

$4$ from

9

$9$ .

m = \frac{5}{4 - (9)}

$m = \frac{5}{4 - (9)}$

m = \frac{5}{4 - (9)}

$m = \frac{5}{4 - (9)}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply

- 1

$- 1$ by

9

$9$ .

m = \frac{5}{4 - 9}

$m = \frac{5}{4 - 9}$

Step 1.4.2.2

Subtract

9

$9$ from

4

$4$ .

m = \frac{5}{- 5}

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

m = \frac{5}{- 5}

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

Step 1.4.3

Divide

5

$5$ by

- 5

$- 5$ .

m = - 1

$m = - 1$

m = - 1

$m = - 1$

m = - 1

$m = - 1$

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 = (- 1) \cdot x + b

$y = (- 1) \cdot x + b$

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 = (- 1) \cdot (9) + b

$y = (- 1) \cdot (9) + b$

Step 2.3

Substitute the value of

y

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

y = m x + b

$y = m x + b$ .

4 = (- 1) \cdot (9) + b

$4 = (- 1) \cdot (9) + b$

Step 2.4

Rewrite the equation as

(- 1) \cdot (9) + b = 4

$(- 1) \cdot (9) + b = 4$ .

(- 1) \cdot (9) + b = 4

$(- 1) \cdot (9) + b = 4$

Step 2.5

Multiply

- 1

$- 1$ by

9

$9$ .

- 9 + b = 4

$- 9 + b = 4$

Step 2.6

Move all terms not containing

b

$b$ to the right side of the equation.

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Step 2.6.1

Add

9

$9$ to both sides of the equation.

b = 4 + 9

$b = 4 + 9$

Step 2.6.2

Add

4

$4$ and

9

$9$ .

b = 13

$b = 13$

b = 13

$b = 13$

b = 13

$b = 13$

Step 3

List the slope and y-intercept.

Slope:

- 1

$- 1$

y-intercept:

(0, 13)

$(0, 13)$

Step 4