Question

a homework assignment is worth a maximum of 60 points. each incorrect answer on the homework assignment results in a deduction of 3 points. the linear function that represents this situation, where x is the number of incorrect answers and y is the total number of points on the homework assignment, is shown on the graph.

Explanation:

Step1: Identify two points

From the graph, we can see two points: when \( x = 0 \), \( y = 60 \) (since the homework is worth a maximum of 60 points with 0 incorrect answers) and when \( x = 20 \), \( y = 0 \) (20 incorrect answers result in 0 points). So the two points are \((0, 60)\) and \((20, 0)\).

Step2: Calculate the slope

The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Substituting the points \((0, 60)\) and \((20, 0)\), we get \( m=\frac{0 - 60}{20 - 0}=\frac{- 60}{20}=- 3 \).

Step3: Determine the equation

The slope - intercept form of a line is \( y=mx + b \), where \( b \) is the y - intercept. We know that when \( x = 0 \), \( y = 60 \), so \( b = 60 \). Since \( m=-3 \), the equation of the line is \( y=-3x + 60 \).

Answer:

The linear function is \( y=-3x + 60 \)