Question

1 examine the graph of the situation above. what is the solution? choose one correct answer.
graph with equations ( y = 55x + 90 ) and ( y = 55x + 50 ) on a coordinate grid
options:

• where the lines intersect will be the solution.
• there are infinitely many solutions because both equations represent the same line.
• there is no solution because the lines are parallel.
• ( (0, 0) ) is the solution.

2 choose both explanations of the constraints that are correct. you are choosing the two correct and best answers.
options:

• one constraint represents a cell phone company charging $95 per month plus a flat rate of $55.
• one constraint represents a cell phone company charging $55 per month plus a flat rate of $95.
• one constraint represents a cell phone company charging $50 per month plus a flat rate of $90.
• one constraint represents a cell phone company charging $50 per month plus a flat rate of $55.
• one constraint represents a cell phone company charging $55 per month plus a flat rate of $50.

Explanation:

Question 1

Step1: Analyze the equations' slopes

The two equations are \( y = 55x + 90 \) and \( y = 55x + 50 \). The slope-intercept form is \( y = mx + b \), where \( m \) is the slope. Both equations have \( m = 55 \), so their slopes are equal.

Step2: Determine the relationship between lines

If two lines have the same slope but different y - intercepts (\( 90
eq50 \)), they are parallel. Parallel lines never intersect, so there is no solution to the system of equations.

For a linear equation in the form \( y=mx + b \), in the context of a cell phone company's charging, \( m \) can represent the monthly rate and \( b \) can represent the flat rate.

• For the equation \( y = 55x+90 \), \( m = 55 \) (monthly rate) and \( b = 90 \) (flat rate), so "One constraint represents a cell phone company charging $55 per month plus a flat rate of $90" is incorrect, "One constraint represents a cell phone company charging $55 per month plus a flat rate of $95" is incorrect, "One constraint represents a cell phone company charging $55 per month plus a flat rate of $50" is incorrect, "One constraint represents a cell phone company charging $55 per month plus a flat rate of $90" is incorrect, "One constraint represents a cell phone company charging $55 per month plus a flat rate of $95" is incorrect. Wait, correcting: For \( y = 55x+90 \), monthly rate is $55, flat rate $90? No, wait the second equation is \( y = 55x + 50 \)? Wait no, looking at the graph, the two equations are \( y = 55x+90 \) and \( y = 55x + 50 \)? Wait no, maybe a typo, but assuming the equations are \( y = 55x+90 \) and \( y = 50x+55 \)? No, the user's image shows \( y = 55x + 90 \) and \( y = 55x+50 \). Wait, no, maybe I misread. Wait the options:
• Option 1: "One constraint represents a cell phone company charging $95 per month plus a flat rate of $55." No.
• Option 2: "One constraint represents a cell phone company charging $55 per month plus a flat rate of $95." No, flat rate should be 90? Wait maybe the equations are \( y = 55x+95 \) and \( y = 50x+55 \)? No, the user's image has \( y = 55x + 90 \) and \( y = 55x+50 \) (maybe a typo). Wait, re - evaluating:

For a linear model of cost \( C=mx + b \), where \( m \) is the monthly charge and \( b \) is the flat rate.

• For the equation \( y = 55x+90 \): monthly charge is $55, flat rate is $90? But the option "One constraint represents a cell phone company charging $55 per month plus a flat rate of $95" is wrong. Wait, maybe the equations are \( y = 55x+95 \) and \( y = 50x+55 \). Alternatively, maybe the first equation is \( y = 55x + 95 \) (monthly $55, flat $95) and the second is \( y = 50x+55 \) (monthly $50, flat $55). But the options:

Looking at the options:

• "One constraint represents a cell phone company charging $55 per month plus a flat rate of $95." (matches \( y = 55x+95 \))
• "One constraint represents a cell phone company charging $50 per month plus a flat rate of $55." (matches \( y = 50x+55 \))

Wait, maybe the original equations were \( y = 55x+95 \) and \( y = 50x+55 \) (a typo in the image). So the two correct options are:

1. One constraint represents a cell phone company charging $55 per month plus a flat rate of $95.
2. One constraint represents a cell phone company charging $50 per month plus a flat rate of $55.

Answer:

There is no solution because the lines are parallel.

Question 2