Question

ready, set, go! name akiyah young period date
ready
topic: applying slope formula
calculate the slope of the line between the given points. use your answer to indicate which line is the steepest.

1. a (-3,7) b (-5,17)
2. h (12,-37) k (4,-3)
3. p (-11,-24) q (21,40)
4. r (55,-75) w (-15,-40)

set
topic: investigating perimeters and areas
adam and his brother are responsible for feeding their horses. in the spring and summer the horses graze in an unfenced pasture. the brothers have erected a portable fence to corral the horses in a grazing area. each day the horses eat all of the grass inside the fence. then the boys move it to a new area where the grass is long and green. the porta - fence consists of 16 separate pieces of fencing each 10 feet long. the brothers have always arranged the fence in a long rectangle with one length of fence on each end and 7 pieces on each side making the grazing area 700 sq. ft. adam has learned in his math class that a rectangle can have the same perimeter but different areas. he is beginning to wonder if he can make his daily job easier by rearranging the fence so that the horses have a bigger grazing area. he begins by making a table of values. he lists all of the possible areas of a rectangle with a perimeter of 160 ft., while keeping in mind that he is restricted by the lengths of his fencing units. he realizes that a rectangle that is oriented horizontally in the pasture will cover a different section of grass than one that is oriented vertically. so he is considering the two rectangles as different in his table. use this information to answer questions 5 - 9 on the next page.
horizontal
vertical

Explanation:

Step1: Recall slope formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Calculate slope for points A(-3,7) and B(-5,17)

$m_1=\frac{17 - 7}{-5-(-3)}=\frac{10}{-2}=- 5$

Step3: Calculate slope for points H(12,-37) and K(4,-3)

$m_2=\frac{-3-(-37)}{4 - 12}=\frac{34}{-8}=-\frac{17}{4}=-4.25$

Step4: Calculate slope for points P(-11,-24) and Q(21,40)

$m_3=\frac{40-(-24)}{21-(-11)}=\frac{64}{32}=2$

Step5: Calculate slope for points R(55,-75) and W(-15,-40)

$m_4=\frac{-40-(-75)}{-15 - 55}=\frac{35}{-70}=-0.5$

Step6: Compare absolute - values of slopes

$|m_1| = 5$, $|m_2|=4.25$, $|m_3| = 2$, $|m_4|=0.5$. Since $5>4.25>2>0.5$, the line between points A and B is the steepest.

Answer:

The line between points A(-3,7) and B(-5,17) is the steepest.