Questions: Find the linear function with the following properties. f(-6)=-4 f(-4)=6

Solution Steps

To find the linear function, we need to determine the slope and the y-intercept. We can use the two given points \((-6, -4)\) and \((-4, 6)\) to calculate the slope. Once we have the slope, we can use one of the points to solve for the y-intercept. The linear function will be in the form \(f(x) = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Using the two points \((-6, -4)\) and \((-4, 6)\), we calculate the slope \(m\) as follows:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - (-4)}{-4 - (-6)} = \frac{10}{2} = 5.0 \]

Next, we use one of the points to find the y-intercept \(b\). Using the point \((-6, -4)\):

\[ b = y_1 - m \cdot x_1 = -4 - 5.0 \cdot (-6) = -4 + 30 = 26.0 \]

Now that we have both the slope and the y-intercept, we can express the linear function \(f(x)\):

\[ f(x) = mx + b = 5.0x + 26.0 \]

Final Answer