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

Question 1:

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

Where:

m: It's the slope It is a point through which the line passes

Thus, the equation is of the form:

We make a point:

Finally, the equation is:

Question 2:

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

Plant 1: (3 was the initial height)

Plant 2: (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:

Option C

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c