Question

Ariel wants to write 8 entries for her blog. After 2 hours, she has 5 entries left. After 4 hours, she has 2 entries left. Which graph represents Ariel's remaining entries?
graph of line going through (0, 0) with a slope of 1.5

graph of line going through (0, 2) with a slope of 2

graph of line going through (0, 8) with a slope of 1.5

graph of line going through (0, 3) with a slope of 3

Answer 1

Let x be a time in hours and y be an amount of remaining entries. You have that:

• At start Ariel wants to write 8 entries for her blog. This means that x=0 and y=8 (0 entries were written). The point with coordinates (0,8) belongs to needed graph.
• After 2 hours, she has 5 entries left. This gives you that at x=2, y=5 and graph passes through the point (2,5).
• After 4 hours, she has 2 entries left. This gives you that at x=4, y=2 and graph passes through the point (4,2).

Find the slope of the line that is passing through the points $(x_1,y_1)$ and $(x_2,y_2)$  by formula

$\dfrac{y_2-y_1}{x_2-x_1}.$

Thus, the slope is

$\dfrac{5-2}{2-4}=-1.5.$

Answer: graph of line going through (0, 8) with a slope of -1.5

Answer 2

graph of line going through (0, 8) with a slope of 1.5 

It is because, between two intervals of two hours, she did the entry for 3 blogs so, 1.5 Blog per hour. and Lower & upper limits are 0 & 8 respectively as mentioned in the question!

Hope this helps!