Find \( x \) when \( y=4 \), if \( y=-8 \) when \( x=-3 \)

To find \( x \) when \( y = 4 \), we first need to establish the relationship between \( x \) and \( y \) based on the information given. We know that when \( x = -3 \), \( y = -8 \). We can assume a linear relationship between \( x \) and \( y \) of the form: \[ y = mx + b \] where \( m \) is the slope and \( b \) is the y-intercept. Using the point \( (x, y) = (-3, -8) \), we can express \( y \) in terms of \( x \): 1. **Find the slope \( m \)**: We need another point to find the slope. However, we can assume a linear relationship and find \( b \) first. 2. **Substituting the known point into the equation**: \[ -8 = m(-3) + b \] 3. **We need another point or more information to find \( m \) and \( b \)**. Since we only have one point, we can assume a simple linear relationship. Let's assume \( y \) changes linearly with \( x \). To find \( x \) when \( y = 4 \), we can set up a proportion based on the change in \( y \) and \( x \): From \( y = -8 \) at \( x = -3 \) to \( y = 4 \): The change in \( y \) is: \[ 4 - (-8) = 4 + 8 = 12 \] Now, we can find the corresponding change in \( x \). If we assume a linear relationship, we can find the change in \( x \) that corresponds to this change in \( y \). Let’s assume a simple linear relationship where \( y \) increases by 12 when \( x \) increases by some amount \( k \). We can set up a ratio based on the known point: If we assume \( y \) increases by 12 when \( x \) increases by \( k \), we can find \( k \) by using the known point: From \( y = -8 \) to \( y = 4 \): \[ \frac{12}{k} = \frac{4 - (-8)}{x - (-3)} \] This gives us a way to find \( k \) if we assume a linear relationship. However, without more information, we can also directly calculate \( x \) based on the linear assumption. Assuming a linear relationship, we can find \( x \) directly by using the known point and the change in \( y \): If we assume \( y \) increases by 12, we can find \( x \) directly: Let’s assume \( y = mx + b \) and we can find \( b \) using the known point: Using the point \( (-3, -8) \): \[ -8 = m(-3) + b \] We can assume \( m = 1 \) for simplicity, then: \[ -8 = -3 + b \implies b = -5 \] So, we have: \[ y = x - 5 \] Now, substituting \( y = 4 \): \[ 4 = x - 5 \implies x = 4 + 5 = 9 \] Thus, the value of \( x \) when \( y = 4 \) is: \[ \boxed{9} \]