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

Answer:

Part A: Option A

Part B: Option C

Step-by-step 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

$slope=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{15-5}{21-7}=\frac{10}{14}=\frac{5}{7}$

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.

$slope=\frac{1}{3}\times \frac{5}{7}=\frac{5}{21}$

The equation of line becomes

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

$y-0=\frac{5}{21}(x-0)$

$21y=5x$

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.

Answer 2

Answer:

part 1 A and part 2 C

Step-by-step explanation: