Question

a line of best fit is also shown on the scatter plot. the equation for the line of best fit is $y = \frac{75}{2}x - 875$.
a customer has a budget of $700 to purchase a new television.
a. based on the customer’s budget and the equation for the line of best fit, what is the largest screen size, in inches, the customer should plan to purchase?

b. explain why the ordered pair $(20, -175)$ in not a solution for this context even though the equation $-175 = \frac{100}{3}(20) - 750$ is true.

Explanation:

Part A

Step1: Substitute y with 700

We know the equation of the line of best fit is \( y = \frac{75}{2}x - 875 \), and the budget (y - value, price) is 700. So we substitute \( y = 700 \) into the equation:
\( 700=\frac{75}{2}x - 875 \)

Step2: Solve for x

First, add 875 to both sides:
\( 700 + 875=\frac{75}{2}x \)
\( 1575=\frac{75}{2}x \)

Then, multiply both sides by \( \frac{2}{75} \) to isolate x:
\( x = 1575\times\frac{2}{75} \)
Simplify \( 1575\div75 = 21 \), then \( 21\times2 = 42 \). So \( x = 42 \).

In this context, \( y \) represents the price of the television, and \( x \) represents the screen size (inches). A negative price (\( y=-175 \)) for a television does not make sense in real - world terms, as the price of a television must be a non - negative value. Even though the ordered pair \((20, - 175)\) satisfies the given equation mathematically, it violates the real - world constraints of the problem (price cannot be negative), so it is not a solution for this context.

Answer:

42 inches

Part B