Question

A line has a slope of 3/5. Which points could this line pass?
A. (-9, 7) and (4, -3)
B. (-7, -2) and (5, 21)
C. (8, 1) and (5, 0)
D. (6, 3) and (11, 6)

Answer 1

To determine which points the line with a slope of 3/5 could pass through, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope of the line, and b is the y-intercept.

We can use the given slope of the line, 3/5, and one of the points to find the y-intercept. Let's use the point (-9, 7):

7 = (3/5)(-9) + b
7 = -27/5 + b
7 + 27/5 = b
(35 + 27)/5 = b
62/5 = b

So the y-intercept is 62/5, or 12.4.

Now, we can substitute the slope, 3/5, and the y-intercept, 12.4, into the slope-intercept form to create the equation of the line: y = (3/5)x + 12.4.

We can check whether the other points satisfy this equation:

Let's check the point (4, -3):
-3 = (3/5)(4) + 12.4
-3 = 12/5 + 12.4
-3 = 12/5 + 62/5
-3 = 74/5

This equation is not satisfied, so the line does not pass through the point (4, -3).

Let's check the point (-7, -2):
-2 = (3/5)(-7) + 12.4
-2 = -21/5 + 62/5
-2 = 41/5

This equation is not satisfied, so the line does not pass through the point (-7, -2).

Let's check the point (5, 21):
21 = (3/5)(5) + 12.4
21 = 3 + 12.4
21 = 15.4

This equation is not satisfied, so the line does not pass through the point (-7, -2).

Let's check the point (8, 1):
1 = (3/5)(8) + 12.4
1 = 24/5 + 62/5
1 = 86/5

This equation is satisfied, so the line passes through the point (8, 1).

Let's check the point (6, 3):
3 = (3/5)(6) + 12.4
3 = 18/5 + 62/5
3 = 80/5

This equation is not satisfied, so the line does not pass through the point (6, 3).

Let's check the point (11, 6):
6 = (3/5)(11) + 12.4
6 = 33/5 + 62/5
6 = 95/5

This equation is not satisfied, so the line does not pass through the point (11, 6).

Therefore, the line with a slope of 3/5 could pass through the points (8, 1) and (5, 0). The correct answer is C.