Question

when bernadine travels for work, her company pays a daily meal allowance of $20.00 and $0.59 per mile she drives. on a certain day, she drives m miles for work and she recieves d dollars from her company to cover her meals and miles that day. which of the following graphs shows the relationship between m and d ?

Explanation:

Step1: Determine the equation

The total allowance \( d \) is the sum of the daily meal allowance (\$20) and the mileage allowance (\$0.59 per mile). So the equation is \( d = 0.59m + 20 \). This is a linear equation in the form \( y = mx + b \), where the slope \( m = 0.59 \) (positive, so the line should have a positive slope) and the y - intercept \( b = 20 \) (when \( m = 0 \), \( d = 20 \), so the graph should cross the d - axis (y - axis) at 20).

Step2: Analyze the graph features

• Y - intercept: The graph should start at \( (0, 20) \) because when she drives 0 miles (\( m = 0 \)), she still gets the \$20 meal allowance.
• Slope: Since the slope is positive (\( 0.59>0 \)), as the number of miles \( m \) increases, the total allowance \( d \) should increase. So we need to look for a linear graph with a positive slope and a y - intercept of 20.

Answer:

The graph should be a straight line with a positive slope, crossing the vertical axis (representing \( d \)) at 20 and increasing as the horizontal axis (representing \( m \)) increases. (To identify the specific graph from options, look for a line with y - intercept 20 and positive slope. For example, if there are options, the correct one will have these two features.)