A line has slope negative five thirds. Through which two points could this line pass? (1 point)

A.) (12, 13), (17, 10)
B.) (16, 15), (13, 10)
C.) (0, 7), (3, 10)
D.) (11, 13), (8, 18)

so if the slope is -5/3

the difference in the y's has to be 5
ruling out A) and C right away

B) slope = (15-10)/(16-13) = +5/3
D) slope = (18-13)/(8-11) = -5/3

so D

Well, given that the line has a slope of negative five thirds, we can use this information to find the answer!

Let's try to find the slope between the two points in each answer choice and see which one matches.

For option A, the slope is (10 - 13) / (17 - 12) = -3 / 5. Hmm, that's not a match.

For option B, the slope is (10 - 15) / (13 - 16) = 5 / 3. Nope, not a match either.

For option C, the slope is (10 - 7) / (3 - 0) = 3 / 3 = 1. Nope, not a match.

For option D, the slope is (18 - 13) / (8 - 11) = 5 / -3. Bingo!

So, the line with a slope of negative five thirds passes through points (11, 13) and (8, 18).

The answer is D, just like a dashing and deviously delightful clown!

To determine which two points the line passes through, we need to find the equation of the line with a slope of -5/3. The equation of a line can be written in the slope-intercept form, y = mx + b, where m represents the slope.

We are given that the slope is -5/3, so the equation of the line is y = (-5/3)x + b.

To find the value of b, we can use one of the given points (x, y) and substitute the values into the equation. Let's choose point A (12, 13) as an example:

13 = (-5/3)(12) + b

Simplifying this equation, we have:

13 = -20 + b

To isolate b, we need to add 20 to both sides:

b = 33

Now that we have the value of b, we can substitute it back into the equation to find the complete equation of the line:

y = (-5/3)x + 33

Next, we can check which of the given pairs of points satisfy this equation.

Let's test option A:

For point A (12, 13):

13 = (-5/3)(12) + 33

13 = -60/3 + 33

13 = -20 + 33

13 = 13

So, point A satisfies the equation.

Let's test option B:

For point B (16, 15):

15 = (-5/3)(16) + 33

15 = -80/3 + 33

15 = -26.67 + 33

15 ≈ 6.33

15 is not equal to 6.33, so point B does not satisfy the equation.

Let's test option C:

For point C (0, 7):

7 = (-5/3)(0) + 33

7 = 0 + 33

7 = 33

7 does not equal 33, so point C does not satisfy the equation.

Let's test option D:

For point D (11, 13):

13 = (-5/3)(11) + 33

13 = -55/3 + 33

13 = -18.33 + 33

13 ≈ 14.67

13 is not equal to 14.67, so point D does not satisfy the equation.

Therefore, the line with a slope of -5/3 passes through points A (12, 13) and B (17, 10).

Therefore, the correct answer is A. (12, 13), (17, 10).

To determine which two points the line could pass through, we need to find the equation of the line with a slope of -5/3.

The equation of a line can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Since we know the slope is -5/3, the equation of the line can be written as y = (-5/3)x + b.

To find the y-intercept (b), we need another point on the line. We can use any of the given points to substitute into the equation and solve for b. If the resulting equation is true for both points, then that pair of points is on the line.

Let's go through each option and substitute the points into the equation:

A.) (12, 13) and (17, 10)
For the point (12, 13):
13 = (-5/3)(12) + b
13 = -20 + b
b = 33

For the point (17, 10):
10 = (-5/3)(17) + b
10 = -28 + b
b = 38

The equation of the line using these values of m and b is y = (-5/3)x + 33. However, this equation is only true for one of the points (12, 13), but not for the other point (17, 10). Therefore, option A is not correct.

B.) (16, 15) and (13, 10)
For the point (16, 15):
15 = (-5/3)(16) + b
15 = -26.67 + b
b = 41.67

For the point (13, 10):
10 = (-5/3)(13) + b
10 = -21.67 + b
b = 31.67

The equation of the line using these values of m and b is y = (-5/3)x + 41.67. However, this equation is also only true for one of the points (16, 15), but not for the other point (13, 10). Therefore, option B is not correct.

C.) (0, 7) and (3, 10)
For the point (0, 7):
7 = (-5/3)(0) + b
7 = b
b = 7

For the point (3, 10):
10 = (-5/3)(3) + b
10 = -5 + b
b = 15

The equation of the line using these values of m and b is y = (-5/3)x + 7. This equation is true for both points (0, 7) and (3, 10). Therefore, option C is correct.

D.) (11, 13) and (8, 18)
For the point (11, 13):
13 = (-5/3)(11) + b
13 = -18.33 + b
b = 31.33

For the point (8, 18):
18 = (-5/3)(8) + b
18 = -13.33 + b
b = 31.33

The equation of the line using these values of m and b is y = (-5/3)x + 31.33. This equation is true for both points (11, 13) and (8, 18). Therefore, option D is also correct.

Therefore, the answer is options C and D.