Problem Solving

Vincen wrote:In a rectangular coordinate system, which of the following points is intersected by the line connected by the coordinates (5,6) and (21,18)?

A. (9,9)
B. (12,12)
C. (13,13)
D. (12,13)
E. (16,15)

One approach is to first find the slope
Slope = (18 - 6)/(21 - 5) = 12/16 = 3/4

IMPORTANT: if the slope is 3/4, then we can start at (5,6) and move up 3 spaces and then move right 4 spaces to find other points on the line (with INTEGER values)

Start at: (5,6)
Move 3 units up and 4 units to the right to get to the point (9,9) (check answer choices - it's there!)

Answer: A

Cheers ,
Brent

Vincen wrote:In a rectangular coordinate system, which of the following points is intersected by the line connected by the coordinates (5,6) and (21,18)?

A. (9,9)
B. (12,12)
C. (13,13)
D. (12,13)
E. (16,15)

Let's first create the equation of a line for coordinates (5,6) and (21,18).

Slope = change in y/change in x = 12/16 = 3/4.

We can substitute in either ordered pair to calculate the y-intercept. Let's use (5,6):

y = (3/4)x + b

6 = (3/4)(5) + b

6 = 15/4 + b

24/4 = 15/4 + b

9/4 = b

Thus, y = (3/4)x + 9/4

Let's now substitute each set of coordinates to see which holds true in our equation.

A) (9,9)

9 = (3/4)(9) + 9/4 ?

9 = 27/4 + 9/4 ?

9 = 36/4 ?

9 = 9 ? ..... Yes!

Answer: A