Question

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

Answer 1

To determine the equation of a line given its slope and two points, we can use the point-slope form: y - y₁ = m(x - x₁), where m is the slope of the line, and (x₁, y₁) are the coordinates of a point on the line.

Let's calculate the equation using option A: (12,13),(17,10)

The slope of the line is -5/3. Let's choose the point (12,13), which gives us:

y - 13 = (-5/3)(x - 12)
y - 13 = (-5/3)x + 20
y = (-5/3)x + 33

If we substitute the coordinates of the other point (17,10) into the equation, we can verify if it satisfies the equation:

10 = (-5/3)(17) + 33
10 = -85/3 + 99/3
10 = 14/3

This equation is not satisfied, so option A is not correct.

Let's check option B: (16,15),(13,10)

Using the same process, we find the equation to be:

y - 15 = (-5/3)(x - 16)
y - 15 = (-5/3)x + 80/3
y = (-5/3)x + 125/3

Substituting the coordinates of the second point:

10 = (-5/3)(13) + 125/3
10 = -65/3 + 125/3
10 = 60/3
10 = 20/3

This equation is not satisfied, so option B is not correct.

Let's check option C: (0,7), (3,10)

Proceeding with the same steps, we get:

y - 7 = (-5/3)(x - 0)
y - 7 = (-5/3)x
y = (-5/3)x + 7

Substituting the values from the second point equation:

10 = (-5/3)(3) + 7
10 = -15/3 + 21/3
10 = 6/3
10 = 2

This equation is not satisfied, so option C is not correct.

Finally, let's check option D: (11,13), (8,18)

Following the same steps as before, we find the equation to be:

y - 13 = (-5/3)(x - 11)
y - 13 = (-5/3)x + 55/3
y = (-5/3)x + 94/3

Now substituting the coordinates of the second point:

18 = (-5/3)(8) + 94/3
18 = -40/3 + 94/3
18 = 54/3
18 = 18

This equation is satisfied, so option D is correct.

Therefore, the line with a slope of -5/3 could pass through points (11,13) and (8,18), making option D the correct answer.