Finite Math Examples

$f (1) = - 1$ , $f (1) = 2$

Step 1

$f (1) = - 1$ , which means $(1, - 1)$ is a point on the line. $f (1) = 2$ , which means $(1, 2)$ is a point on the line, too.

$(1, - 1), (1, 2)$

Step 2

Find the slope of the line between $(1, - 1)$ and $(1, 2)$ 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.

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

Step 2.4

Simplify.

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Step 2.4.1

Multiply $- 1$ by $1$ .

$\frac{2 - (- 1)}{1 - 1}$

Step 2.4.2

Subtract $1$ from $1$ .

$\frac{2 - (- 1)}{0}$

Step 2.4.3

The expression contains a division by $0$ . The expression is undefined.

Undefined

Step 3

The slope of the line is undefined, which means that it is perpendicular to the x-axis at $x = 1$ .

$x = 1$

Step 4

The final answer is the equation in slope-intercept form.

$y = 1$

Step 5

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

$f (x) = 1$

Step 6