Pre-Algebra Examples

(1, - 2)

$(1, - 2)$ ,

(3, 6)

$(3, 6)$

Step 1

Find the slope of the line between

(1, - 2)

$(1, - 2)$ and

(3, 6)

$(3, 6)$ using

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

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of

y

$y$ over the change of

x

$x$ .

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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{6 - (- 2)}{3 - (1)}

$m = \frac{6 - (- 2)}{3 - (1)}$

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

- 2

$- 2$ .

m = \frac{6 + 2}{3 - (1)}

$m = \frac{6 + 2}{3 - (1)}$

Step 1.4.1.2

Add

6

$6$ and

2

$2$ .

m = \frac{8}{3 - (1)}

$m = \frac{8}{3 - (1)}$

m = \frac{8}{3 - (1)}

$m = \frac{8}{3 - (1)}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply

- 1

$- 1$ by

1

$1$ .

m = \frac{8}{3 - 1}

$m = \frac{8}{3 - 1}$

Step 1.4.2.2

Subtract

1

$1$ from

3

$3$ .

m = \frac{8}{2}

$m = \frac{8}{2}$

m = \frac{8}{2}

$m = \frac{8}{2}$

Step 1.4.3

Divide

8

$8$ by

2

$2$ .

m = 4

$m = 4$

m = 4

$m = 4$

m = 4

$m = 4$

Step 2

Use the slope

4

$4$ and a given point

(1, - 2)

$(1, - 2)$ to substitute for

x_{1}

$x_{1}$ and

y_{1}

$y_{1}$ in the point-slope form

y - y_{1} = m (x - x_{1})

$y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation

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

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

y - (- 2) = 4 \cdot (x - (1))

$y - (- 2) = 4 \cdot (x - (1))$

Step 3

Simplify the equation and keep it in point-slope form.

y + 2 = 4 \cdot (x - 1)

$y + 2 = 4 \cdot (x - 1)$

Step 4

Solve for

y

$y$ .

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Step 4.1

Simplify

4 \cdot (x - 1)

$4 \cdot (x - 1)$ .

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Step 4.1.1

Rewrite.

y + 2 = 0 + 0 + 4 \cdot (x - 1)

$y + 2 = 0 + 0 + 4 \cdot (x - 1)$

Step 4.1.2

Simplify by adding zeros.

y + 2 = 4 \cdot (x - 1)

$y + 2 = 4 \cdot (x - 1)$

Step 4.1.3

Apply the distributive property.

y + 2 = 4 x + 4 \cdot - 1

$y + 2 = 4 x + 4 \cdot - 1$

Step 4.1.4

Multiply

4

$4$ by

- 1

$- 1$ .

y + 2 = 4 x - 4

$y + 2 = 4 x - 4$

y + 2 = 4 x - 4

$y + 2 = 4 x - 4$

Step 4.2

Move all terms not containing

y

$y$ to the right side of the equation.

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Step 4.2.1

Subtract

2

$2$ from both sides of the equation.

y = 4 x - 4 - 2

$y = 4 x - 4 - 2$

Step 4.2.2

Subtract

2

$2$ from

- 4

$- 4$ .

y = 4 x - 6

$y = 4 x - 6$

y = 4 x - 6

$y = 4 x - 6$

y = 4 x - 6

$y = 4 x - 6$

Step 5

List the equation in different forms.

Slope-intercept form:

y = 4 x - 6

$y = 4 x - 6$

Point-slope form:

y + 2 = 4 \cdot (x - 1)

$y + 2 = 4 \cdot (x - 1)$

Step 6

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