coordinate

[sud21]

[Anurag@Gurome]

Slope of the line passing through (0, 25) and (60, 0) = (0 - 25)/(60 - 0) = -25/60 = -5/12
Equation of line is given by: (y - y1) = m(x - x1), where m is the slope and (x1, y1) is the point through which the lines passes.
So, equation of line is (y - 25) = -5/12(x - 0) or y - 25 = -5x/12
y = 25 - 5x/12
Now the possible ways in which both sides can be integers are when 5/12x is an integer.
So, the possible coordinates are (0, 25), (12, 20), (24, 15), (36, 10), (48, 5), and (60, 0), which means there are 6 coordinates when both x and y are integers.

The correct answer is B.

[Whitney Garner]

Hi sud21!

Many of us might not remember back to our first lessons in geometry, but one of the ways we learned to draw lines on the coordinate plane was to use Slope = Rise over Run...and literally just count blocks and draw dots. We can do that here. The rise of our line (y distance from leftmost point to the rightmost point) is -25, and the run (x distance) is 60, so the slope is -25/60 or -5/12. If we were going to draw a line with slope -5/12, we would start with any given point, then move down 5 and over 12 to draw the next point. Since we will start at (0,25) and then draw a new point every time we fall 5 (5 goes into 25, 5 times), we will draw 5 more points. So that leaves 6 points on the line that are whole numbers!


Whit