Precalculus Examples

$(1, 2)$ , $(3, 4)$

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.

$m = \frac{4 - (2)}{3 - (1)}$

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 $- 1$ by $2$ .

$m = \frac{4 - 2}{3 - (1)}$

Step 1.4.1.2

Subtract $2$ from $4$ .

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

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $1$ .

$m = \frac{2}{3 - 1}$

Step 1.4.2.2

Subtract $1$ from $3$ .

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

Step 1.4.3

Divide $2$ by $2$ .

$m = 1$

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, $y = m x + b$ .

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

Step 2.2

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

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

Step 2.3

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

$2 = (1) \cdot (1) + b$

Step 2.4

Rewrite the equation as $(1) \cdot (1) + b = 2$ .

$(1) \cdot (1) + b = 2$

Step 2.5

Multiply $1$ by $1$ .

$1 + b = 2$

Step 2.6

Move all terms not containing $b$ to the right side of the equation.

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Step 2.6.1

Subtract $1$ from both sides of the equation.

$b = 2 - 1$

Step 2.6.2

Subtract $1$ from $2$ .

$b = 1$

Step 3

List the slope and y-intercept.

Slope: $1$

y-intercept: $(0, 1)$

Step 4

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