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

Answer:

Graph of line going through (0, 8) with a slope of 1.5  represents Ariel's remaining entries

Step-by-step explanation:

Ariel wants to write 8 entries for her blog.

After 2 hours, she has 5 entries left. $(x_1,y_1)=(2,5)$

After 4 hours, she has 2 entries left. $(x_2,y_2)=(4,2)$

So, now using two point slope form:

$y-y_1=m(x-x_1)$ ---1

where $m = \frac{y_2-y_1}{x_2-x_1}$

So , substituting the given points we get the equation that represents the given situation .

$m = \frac{2-5}{4-2}$

$m = \frac{-3}{2}$

$m = -1.5$

Now,

$y-5 = -1.5(x-2)$

$y-5 = -1.5x+3$

Thus the slope of the given situation is 1.5

Now at x = 0

$y-5 = -1.5*0+3$

$y=8$

So, at 0 hour 8 entries left .

So, graph of line going through (0, 8) with a slope of 1.5  represents Ariel's remaining entries

Answer 2

After 2 hours she wrote 3 entries.
after 4 hours she wrote 6 entries.
This means that for same period she is writing same number of entries which means her "writing speed" is constant.
that means that graph is linear function (straight line).

slope we calculate by putting coordinates of y and x of any dot on that line. we can use one of those given by text of task. (in 2 hours she wrote 3 entries)
y = k*x
k = y/x
k = 1.5