MATH SOLVE

3 months ago

Q:
# 1. Write the equation of the line passing through the points (−1, 2) and (3, 4)A. y = 2x − 2B. y = 2x − 10C. y = 1/2x + 5/2D. y = 1/2x − 5/22. 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 > 1.3B. 4.3 > 3C. 1.3 = 1.3D. 3 = 3

Accepted Solution

A:

Question 1:For this case we have that by definition, the point-slope equation of a line is given by:[tex]y-y_ {0} = m (x-x_ {0})[/tex]Where:m: It's the slope[tex](x_ {0}, y_ {0}):[/tex] It is a point through which the line passes[tex](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}[/tex]Thus, the equation is of the form:[tex]y-y_ {0} = \frac {1} {2} (x-x_ {0})[/tex]We make a point:[tex]y-4 = \frac {1} {2} (x-3)[/tex]Finally, the equation is:[tex]y-4 = \frac {1} {2} (x-3)[/tex]ANswer:[tex]y-4 = \frac {1} {2} (x-3)[/tex]Question 2:For this case we have the following comparison, after one week:Plant 1: [tex]3 + 1.3 = 4.3[/tex](3 was the initial height)Plant 2: [tex]h = 1.3 (1) + 3 = 1.3 + 3 = 4.3[/tex] (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:[tex]1.3 = 1.3[/tex]Answer:Option C