Question

the wrestling team is participating in a competition. the team entrance fee is $1,850, and each wrestler, x, pays an additional $160. write the equation in slope - intercept form that represents the total cost, y, of attending the competition.
$y = 160x + 1,850$
$y = 1,850x + 160$
$y = 1,850x - 160$
$y = 160x - 1,850$

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope (rate of change) and \(b\) is the y - intercept (initial value).

Step2: Identify \(m\) and \(b\) from the problem

• The initial cost (team entrance fee) is a fixed cost, which is the y - intercept \(b\). Here, the team entrance fee is \(\$1850\), so \(b = 1850\).
• The cost per wrestler (\(x\)) is the rate of change, which is the slope \(m\). Each wrestler pays \(\$160\), so \(m = 160\).

Step3: Substitute \(m\) and \(b\) into the slope - intercept form

Substituting \(m = 160\) and \(b = 1850\) into \(y=mx + b\), we get \(y=160x + 1850\).

Answer:

\(y = 160x+1850\) (the first option among the given choices)