QuestionFunction $A$ and Function $B$ are linear functions.
Function A
Function B \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 3 & 2 \\ \hline 6 & 3 \\ \hline 9 & 4 \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. Function $A$ is a linear function with a line passing through the points $(-10, -10)$ and $(10, 10)$ .
2. Function $B$ is a linear function with given points $(3, 2)$ , $(6, 3)$ , and $(9, 4)$ .
3. We need to determine the equations of both linear functions.

STEP 2

1. Determine the equation of Function $A$ .
2. Determine the equation of Function $B$ .

STEP 3

To find the equation of Function $A$ , use the two points $(-10, -10)$ and $(10, 10)$ .
Calculate the slope $m$ using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
Substitute the points: $m = \frac{10 - (-10)}{10 - (-10)} = \frac{20}{20} = 1$

STEP 4

With the slope $m = 1$ , use the point-slope form $y - y_1 = m(x - x_1)$ with point $(-10, -10)$ :
$y - (-10) = 1(x - (-10))$
Simplify to get the equation of Function $A$ : $y + 10 = x + 10$ $y = x$

STEP 5

To find the equation of Function $B$ , use the points $(3, 2)$ and $(6, 3)$ .
Calculate the slope $m$ using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
Substitute the points: $m = \frac{3 - 2}{6 - 3} = \frac{1}{3}$

STEP 6

With the slope $m = \frac{1}{3}$ , use the point-slope form $y - y_1 = m(x - x_1)$ with point $(3, 2)$ :
$y - 2 = \frac{1}{3}(x - 3)$
Simplify to get the equation of Function $B$ : $y - 2 = \frac{1}{3}x - 1$ $y = \frac{1}{3}x + 1$
The equations of the functions are: - Function $A$ : $y = x$ - Function $B$ : $y = \frac{1}{3}x + 1$

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