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Instructions:Select the correct answer from each drop-down menu.

The slope of the line passing through the points (7, 5) and (21, 15) is _____.
A.) 5/7
B.) 7/5
C.) 5
D.) 7

Another line with a slope that is one-third that of the slope you just calculated passes through the origin and the point _____.
A.) (3, 5)
B.) (3, 7)
C.) (21, 5)
D.) (21, 7)

User MR Zamani
by
8.5k points

2 Answers

5 votes

Answer:

part 1 A and part 2 C

Explanation:

User Yassine Elouafi
by
7.8k points
3 votes

Answer:

Part A: Option A

Part B: Option C

Explanation:

Given two points (7, 5) and (21, 15)

we have to find the slope of the line passing through above two points.

The slope of line can be calculated as


slope=(y_2-y_1)/(x_2-x_1)


m=(15-5)/(21-7)=(10)/(14)=(5)/(7)

Option A is correct.

Part B: Also given another line with a slope that is one-third that of the slope of above and passes through the origin and the point

we have to find the point.


slope=(1)/(3)* (5)/(7)=(5)/(21)

The equation of line becomes


y-y'=m(x-x')


y-0=(5)/(21)(x-0)


21y=5x

The point which satisfies the above equation passes through the line.


(3,5):21(5)=5(3) Not satisfied


(3,7):21(7)=5(3) Not satisfied


(21,5):21(5)=5(21) Satisfied


(21,7):21(7)=2(21) Not satisfied

Hence, the line passes through the point (21, 5)

Option C is correct.

User Anthony Bishopric
by
7.7k points

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