Question

1. (3 pts) the table below shows the hours, x, spent working on a new road and the distance, y, of the finished road.

time (hours) distance(miles)
50 1.5
200 6
350 10.5
400 12
650 19.5
part a. what is the slope of the line that fits these data?
a. $\frac{3}{400}$
b. $\frac{3}{100}$
c. $\frac{3}{25}$
d. 3
part b. what is the meaning of the slope?
part c. what is the meaning of the y - intercept?

1. (2 pts) given the points (3,5), (2,4), (9,0), and (?, 6), what could replace the ? to create a relation that is not a function?

a. 1
b. 3
c. 4
d. 7

1. (3 pts)

x -4 -3 0 -3
y 8 1 -5 2
domain?
range?
is it a function? yes / no

1. (3 pts)

is the graph above a function?
explain why or why not:

1. (2 pts) the function a(n) = represents the value of the nth term of a sequence. what is the sum of the 5th terms of the sequence?
2. (3 pts)

domain?
range?
is it a function? yes / no

Explanation:

8.

Part A

Step1: Recall slope formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two - points from the table, say $(x_1,y_1)=(50,1.5)$ and $(x_2,y_2)=(200,6)$.

Step2: Substitute values into formula

$m=\frac{6 - 1.5}{200 - 50}=\frac{4.5}{150}=\frac{45}{1500}=\frac{3}{100}$

The slope represents the rate of change. In this context, for every 100 hours of work, 3 miles of the road are completed.

The y - intercept would represent the distance of the finished road when no time has been spent working (i.e., $x = 0$). In a real - world scenario, if there is no work done, the distance of the finished road is 0, so the y - intercept is 0, meaning no road is finished when no work is done.

Answer:

B. $\frac{3}{100}$

Part B