Question

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)

Answer 1

part 1 A and part 2 C

Explanation:

Answer 2

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.