Question

1. Write the equation of the line passing through the points (−1, 2) and (3, 4)

A. y = 2x − 2
B. y = 2x − 10
C. y = 1/2x + 5/2
D. y = 1/2x − 5/2

2. A cayenne pepper plant's height when purchased was 3 inches. One week later, the plant 's height was exactly 4.3 inches. A bell pepper plant was also purchased at a height of 3 inches. Its height, h, after x weeks of growth is represented by h = 1.3x + 3. Assuming both plants continue to grow at a constant rate, which statement BEST compares the rate of change per week of the pepper plants?

A. 3 > 1.3
B. 4.3 > 3
C. 1.3 = 1.3
D. 3 = 3

Answer 1

Question 1:

For this case we have that by definition, the point-slope equation of a line is given by:

`y-y_ {0} = m (x-x_ {0})`

Where:

m: It's the slope
`(x_ {0}, y_ {0}):` It is a point through which the line passes

`(x1, y1): (- 1,2)\\(x2, y2) :( 3,4)\\m = \frac {y2-y1} {x2-x1} = \frac {4-2} {3 - (- 1)} = \frac {2} {3 + 1} = \frac {2} {4} = \frac {1} {2}`

Thus, the equation is of the form:

`y-y_ {0} = \frac {1} {2} (x-x_ {0})`

We make a point:

`y-4 = \frac {1} {2} (x-3)`

Finally, the equation is:

`y-4 = \frac {1} {2} (x-3)`

ANswer:

`y-4 = \frac {1} {2} (x-3)`

Question 2:

For this case we have the following comparison, after one week:

Plant 1:
`3 + 1.3 = 4.3`(3 was the initial height)

Plant 2:
`h = 1.3 (1) + 3 = 1.3 + 3 = 4.3` (3 was the initial height)

It is observed that in one week each plant grew 1.3 inches.

Thus, the statement that best compares this situation is:

`1.3 = 1.3`

Answer:

Option C