Algebra Examples

$f (0) = 3$ and $f (- 6) = 3$

Step 1

$f (0) = 3$ , which means $(0, 3)$ is a point on the line. $f (- 6) = 3$ , which means $(- 6, 3)$ is a point on the line, too.

$(0, 3), (- 6, 3)$

Step 2

Find the slope of the line between $(0, 3)$ and $(- 6, 3)$ using $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of $y$ over the change of $x$ .

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Step 2.1

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 2.2

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 2.3

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{3 - (3)}{- 6 - (0)}$

Step 2.4

Simplify.

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Step 2.4.1

Simplify the numerator.

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Step 2.4.1.1

Multiply $- 1$ by $3$ .

$m = \frac{3 - 3}{- 6 - (0)}$

Step 2.4.1.2

Subtract $3$ from $3$ .

$m = \frac{0}{- 6 - (0)}$

Step 2.4.2

Simplify the denominator.

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Step 2.4.2.1

Multiply $- 1$ by $0$ .

$m = \frac{0}{- 6 + 0}$

Step 2.4.2.2

Add $- 6$ and $0$ .

$m = \frac{0}{- 6}$

Step 2.4.3

Divide $0$ by $- 6$ .

$m = 0$

Step 3

Use the slope $0$ and a given point $(0, 3)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (3) = 0 \cdot (x - (0))$

Step 4

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

$y - 3 = 0 \cdot (x + 0)$

Step 5

Solve for $y$ .

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Step 5.1

Simplify $0 \cdot (x + 0)$ .

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Step 5.1.1

Add $x$ and $0$ .

$y - 3 = 0 \cdot x$

Step 5.1.2

Multiply $0$ by $x$ .

$y - 3 = 0$

Step 5.2

Add $3$ to both sides of the equation.

$y = 3$

Step 6

Replace $y$ by $f (x)$ .

$f (x) = 3$

Step 7