Questions: Function A and Function B are linear functions x y ------ 4 8 6 14 9 23 Function B y=5x-2

Solution Steps

To find the equation of Function A, we need to determine the slope and y-intercept of the line that passes through the given points. We can use the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\), which is \((y_2 - y_1) / (x_2 - x_1)\). Once we have the slope, we can use one of the points to solve for the y-intercept using the equation \(y = mx + b\).

Using the points \((4, 8)\) and \((6, 14)\), we calculate the slope \(m\) of Function A as follows:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{14 - 8}{6 - 4} = \frac{6}{2} = 3.0 \]

Next, we use the slope and one of the points to find the y-intercept \(b\). Using the point \((4, 8)\):

\[ b = y - mx = 8 - 3.0 \cdot 4 = 8 - 12 = -4.0 \]

Now that we have both the slope and the y-intercept, we can write the equation of Function A:

\[ y = 3.0x - 4.0 \]

Final Answer