Questions: This table of values represents a linear function. x y ------ -3 14 2 -1 7 -16 a. What is the slope? m= b. What is the y-intercept? b= c. Enter an equation in the form y=mx+b that represents the function defined by this table of values.

This table of values represents a linear function.

x y
------
-3 14
2 -1
7 -16

a. What is the slope? m=
b. What is the y-intercept? b=
c. Enter an equation in the form y=mx+b that represents the function defined by this table of values.

Transcript text: This table of values represents a linear function. \begin{tabular}{|c|c|} \hline $\boldsymbol{x}$ & $\boldsymbol{y}$ \\ \hline-3 & 14 \\ \hline 2 & -1 \\ \hline 7 & -16 \\ \hline \end{tabular} a. What is the slope? $m=$ $\square$ b. What is the $y$-intercept? $b=$ $\square$ c. Enter an equation in the form $y=m x+b$ that represents the function defined by this table of values. $\square$

Solution

Solution Steps

Solution Approach

To find the slope $ m $ of the linear function, use the formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$: $ m = \frac{y_2 - y_1}{x_2 - x_1} $. Choose any two points from the table to calculate the slope. Once the slope is determined, use one of the points and the slope to solve for the $ y $-intercept $ b $ using the equation $ y = mx + b $. Finally, write the equation of the line in the form $ y = mx + b $.

Step 1: Calculate the Slope

To find the slope $ m $ of the linear function, we use the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points $(-3, 14)$ and $(2, -1)$: \[ m = \frac{-1 - 14}{2 - (-3)} = \frac{-15}{5} = -3.0 \]

Step 2: Calculate the $ y $-Intercept

Next, we calculate the $ y $-intercept $ b $ using the slope and one of the points. We can use the point $(-3, 14)$: \[ b = y - mx = 14 - (-3)(-3) = 14 - 9 = 5.0 \]

Step 3: Write the Equation of the Line

Now that we have both $ m $ and $ b $, we can write the equation of the line in the form $ y = mx + b $: \[ y = -3.0x + 5.0 \]