Question

A line has slope - 5/3 Through which two points could this line pass? (1 point) (12, 13); (17, 10); (16, 15); (13, 10); (0, 7); (3, 10); (11, 13); (8, 18)

Answer 1

To determine which two points the line could pass through, we need to find the points that satisfy the given slope.

The slope of a line is given by the formula:

m = (y2 - y1) / (x2 - x1)

Given that the slope is -5/3, we can set up the equation:

-5/3 = (y2 - y1) / (x2 - x1)

Now we can substitute the coordinates of each given point into the equation to see if they satisfy the equation.

Let's try each pair of points:

1) (12, 13) and (17, 10):
m = (10 - 13) / (17 - 12)
m = -3 / 5
This slope does not match -5/3, so these points are not on the line.

2) (17, 10) and (16, 15):
m = (15 - 10) / (16 - 17)
m = 5 / -1 = -5
This slope does not match -5/3, so these points are not on the line.

3) (16, 15) and (13, 10):
m = (10 - 15) / (13 - 16)
m = -5 / -3 = 5/3
This slope matches -5/3, so these points are on the line.

4) (13, 10) and (0, 7):
m = (7 - 10) / (0 - 13)
m = -3 / -13 = 3/13
This slope does not match -5/3, so these points are not on the line.

5) (0, 7) and (3, 10):
m = (10 - 7) / (3 - 0)
m = 3 / 3 = 1
This slope does not match -5/3, so these points are not on the line.

6) (3, 10) and (11, 13):
m = (13 - 10) / (11 - 3)
m = 3 / 8
This slope does not match -5/3, so these points are not on the line.

7) (11, 13) and (8, 18):
m = (18 - 13) / (8 - 11)
m = 5 / -3
This slope does not match -5/3, so these points are not on the line.

Out of the options given, the line could pass through the points (16, 15) and (13, 10).