Question

1. a horizontal line passes through the points (1, -5/2) and (7, j). what is the value of j?
2. one week dell worked 15 hours and made $375. the next week he worked 19 hours and also made $375.

a. how many additional hours did he work in the second week?
b. how much additional pay did he get in the second week?
c. the given information can be written as two points, where x is the number of hours dell works and y is the amount of money he makes in dollars. find the slope of the line that passes through these two points.
d. do you think this situation is reasonable? why or why not?

Explanation:

Step1: Recall property of horizontal line

All points on a horizontal line have the same y - coordinate.

Step2: Identify y - coordinates

The y - coordinate of the first point is $-\frac{5}{2}$. Since the line is horizontal, the y - coordinate of the second point $(7,j)$ is the same as that of the first point. So $j = -\frac{5}{2}$.

Step3: Calculate additional hours for question 6a

The number of hours worked in the first week is 15 and in the second week is 19. The additional hours worked in the second week is $19 - 15=4$ hours.

Step4: Calculate additional pay for question 6b

He made $375$ in the first week and $375$ in the second week. The additional pay is $375 - 375 = 0$ dollars.

Step5: Calculate slope for question 6c

The two points are $(15,375)$ and $(19,375)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $x_1 = 15,y_1 = 375,x_2 = 19,y_2 = 375$ into the formula, we get $m=\frac{375 - 375}{19 - 15}=\frac{0}{4}=0$.

Step6: Analyze situation for question 6d

This situation is reasonable. It could be that Dell has a fixed - salary or a bonus structure that does not depend on the number of hours worked within a certain range, or he might have reached an overtime cap and additional hours do not result in extra pay.

Answer:

1. $j = -\frac{5}{2}$
2. a. 4 hours

b. 0 dollars
c. 0
d. This situation is reasonable. It could be that Dell has a fixed - salary or a bonus structure that does not depend on the number of hours worked within a certain range, or he might have reached an overtime cap and additional hours do not result in extra pay.