We are given data for two linear functions, Function A (in a table) and Function B (in a graph). We need to find the slopes of both functions. Then we need to write the equation of a third linear function $y = mx + b$ such that its slope $m$ is an integer that falls between the slopes of Function A and Function B. We are also restricted to using only integer values.

1. Problem Description

We are given data for two linear functions, Function A (in a table) and Function B (in a graph). We need to find the slopes of both functions. Then we need to write the equation of a third linear function $y = mx + b$ such that its slope $m$ is an integer that falls between the slopes of Function A and Function B. We are also restricted to using only integer values.

2. Solution Steps

First, we find the slope of Function A. We can use the points $(-2, -3)$ and $(0, 5)$.

The slope $m_A$ is calculated as:

$m_A = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - (-3)}{0 - (-2)} = \frac{8}{2} = 4$

Next, we find the slope of Function B from the graph. We can pick two points that appear to lie on the line, such as $(0, 2)$ and $(2, 4)$.

The slope $m_B$ is calculated as:

$m_B = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 2}{2 - 0} = \frac{2}{2} = 1$

Alternatively, using points $(-2, 0)$ and $(0, 2)$:

$m_B = \frac{2 - 0}{0 - (-2)} = \frac{2}{2} = 1$

We seek a slope $m$ for a third function such that $1 < m < 4$. Since $m$ must be an integer, the possible values for $m$ are 2 and

3. We can arbitrarily choose $m = 2$. Since the problem does not specify the y-intercept $b$, we can choose any integer value for $b$. A simple choice is $b = 0$.

So, a possible equation for the third function is $y = 2x + 0$, which simplifies to $y = 2x$.

3. Final Answer

$y = 2x + 0$