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.

Solution Steps

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 $y = mx + b$.

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 $(2, -1)$: $$m = \frac{-1 - 14}{2 - (-3)} = \frac{-15}{5} = -3.0$$

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

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

Final Answer