Question

ron has several solar panels on the roof of his garage and plans to add more solar panels to the roof of his house. the total amount of energy his solar panels will produce on a sunny day depends on how many new solar panels ron adds. this situation can be modeled as a linear relationship.

Explanation:

Step1: Identify the y-intercept

The line crosses the y - axis at (0, 600). So the y - intercept \(b = 600\).

Step2: Calculate the slope

We can use two points, say (0, 600) and (4, 1200). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the values: \(m=\frac{1200 - 600}{4 - 0}=\frac{600}{4}=150\).

Step3: Write the linear equation

The slope - intercept form of a linear equation is \(y=mx + b\). Substituting \(m = 150\) and \(b = 600\), we get \(y = 150x+600\). (If we want to find energy for a certain number of panels, we can substitute \(x\) in this equation. For example, if \(x = 10\), \(y=150\times10 + 600=1500 + 600 = 2100\))

Answer:

The linear equation modeling the relationship is \(y = 150x+600\) (where \(x\) is the number of solar panels added and \(y\) is the total energy produced). If we assume the question is to find the equation, this is the answer. If it's to find energy for a specific number of panels, substitute \(x\) into this equation.