A line has a slope of -3/5. Through which two points could this line pass?
A. (-4, -1) and (3,20)
B. (8,1) and (13,4)
C. (-16, -4) and (12,8)
D. (-5,9) and (10,0)
We can use the slope-intercept form of a line, which is $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. Since the problem does not give us the $y$-intercept, we can choose two sets of points and solve for $b$ to find the equation of the line.
Let's use points A: $(-4, -1)$ and B: $(3,20)$.
We have the slope $m = -\frac{3}{5}$, so replacing $x$ and $y$ with the coordinates of point A, we get $-1 = -\frac{3}{5} \cdot -4 + b$.
Simplifying the equation gives us $-1 = \frac{12}{5} + b$.
Subtracting $\frac{12}{5}$ from both sides gives us $-\frac{17}{5} = b$.
So the equation of the line passing through points A and B is $y = -\frac{3}{5}x - \frac{17}{5}$.
Checking points A and B in this equation:
For A: $-1 = -\frac{3}{5} \cdot -4 - \frac{17}{5} = -\frac{12}{5} - \frac{17}{5} = \frac{-29}{5} = -1$, which is correct.
For B: $20 = -\frac{3}{5} \cdot 3 - \frac{17}{5} = -\frac{9}{5} - \frac{17}{5} = \frac{-26}{5} = -\frac{26}{5}$, which is incorrect.
Therefore, the line does not pass through points A and B. Let's check the other choices.
Using points C: $(-16, -4)$ and D: $(12,8)$:
We have the slope $m = -\frac{3}{5}$, so replacing $x$ and $y$ with the coordinates of point C, we get $-4 = -\frac{3}{5} \cdot -16 + b$.
Simplifying gives us $-4 = \frac{48}{5} + b$.
Subtracting $\frac{48}{5}$ from both sides gives us $-\frac{28}{5} = b$.
So the equation of the line passing through points C and D is $y = -\frac{3}{5}x - \frac{28}{5}$.
Checking points C and D in this equation:
For C: $-4 = -\frac{3}{5} \cdot -16 - \frac{28}{5} = \frac{48}{5} - \frac{28}{5} = \frac{20}{5} = 4$, which is incorrect.
For D: $8 = -\frac{3}{5} \cdot 12 - \frac{28}{5} = -\frac{36}{5} - \frac{28}{5} = \frac{-64}{5} = -\frac{64}{5}$, which is correct.
Therefore, the line does not pass through points C and D either.
Finally, using points E: $(-5,9)$ and F: $(10,0)$:
We have the slope $m = -\frac{3}{5}$, so replacing $x$ and $y$ with the coordinates of point E, we get $9 = -\frac{3}{5} \cdot -5 + b$.
Simplifying gives us $9 = \frac{15}{5} + b$.
Subtracting $\frac{15}{5}$ from both sides gives us $\frac{10}{5} = b$.
So the equation of the line passing through points E and F is $y = -\frac{3}{5}x + \frac{10}{5}$, which simplifies to $y = -\frac{3}{5}x + 2$.
Checking points E and F in this equation:
For E: $9 = -\frac{3}{5} \cdot -5 + 2 = \frac{15}{5} + \frac{10}{5} = \frac{25}{5} = 5$, which is incorrect.
For F: $0 = -\frac{3}{5} \cdot 10 + 2 = -\frac{30}{5} + \frac{10}{5} = \frac{-20}{5} = -4$, which is correct.
Therefore, the line does not pass through points E and F either.
In conclusion, none of the given choices have a line that passes through two points with a slope of $-\frac{3}{5}$.
$\boxed{\text{(None of the above)}}$