Question

a garden center sells trees (x) for $30 each and shrubs (y) for $15 each, with total sales of $450, represented by the equation 30x + 15y = 450. which of the following is the meaning of the x-intercept?

the x-intercept is the number of shrubs sold when zero trees were sold.

the x-intercept is the number of trees sold when zero shrubs were sold.

the x-intercept is 450 trees sold.

the x-intercept is where an equal amount of trees and shrubs was sold.

Explanation:

Step1: Recall the definition of x - intercept

The x - intercept of a function \(y = f(x)\) (or in the equation \(Ax+By = C\)) is found by setting \(y = 0\) and solving for \(x\).

Step2: Apply the definition to the given equation

Given the equation \(30x + 15y=450\). To find the x - intercept, set \(y = 0\). Then the equation becomes \(30x+15\times0 = 450\), i.e., \(30x=450\), and \(x = 15\). Here, \(x\) represents the number of trees sold and \(y\) represents the number of shrubs sold. When \(y = 0\) (zero shrubs sold), we solve for \(x\) (the number of trees sold).

Answer:

The x - intercept is the number of trees sold when zero shrubs were sold.