Question

enter the rise and run to find the slope between points a and b. slope from a to b = rise/?

Explanation:

Step1: Identify coordinates of A and B

Point A is at (2, 1), Point B is at (6, 3).

Step2: Calculate rise (Δy)

Rise = \( 3 - 1 = 2 \)

Step3: Calculate run (Δx)

Run = \( 6 - 2 = 4 \)

Step4: Find slope (rise/run)

Slope = \( \frac{2}{4} = \frac{1}{2} \), but the problem has a negative sign? Wait, no, the line is increasing, maybe a typo? Wait, looking at the graph, from A(2,1) to B(6,3), rise is 2, run is 4. Wait, the problem shows "slope from A to B = -□/□"? Wait, maybe I misread. Wait, no, the line is going up, so slope should be positive. Wait, maybe the user's problem has a typo, but let's check coordinates again. A(2,1), B(6,3). So rise is 3 - 1 = 2, run is 6 - 2 = 4. So slope is 2/4 = 1/2. But the problem has a negative sign. Wait, maybe the points are different? Wait, no, the graph: A is at (2,1), B at (6,3), C at (8,4). Wait, maybe the user made a mistake in the negative sign. But according to the graph, the slope is positive. So rise is 2, run is 4. So the numerator (rise) is 2, denominator (run) is 4? Wait, but the problem says "slope from A to B = -□/□". Wait, maybe the points are A(6,3) to B(2,1)? Then rise would be 1 - 3 = -2, run 2 - 6 = -4, slope (-2)/(-4)=1/2. But if going from A to B as (2,1) to (6,3), rise is 2, run 4. So maybe the negative sign is a mistake. But following the graph, rise is 2, run is 4. So the numerator is 2, denominator 4? Wait, but 2/4 simplifies to 1/2, but the problem has a box for numerator and denominator. So maybe the answer is 2/4, so numerator 2, denominator 4. Or simplified, 1/2. But let's check again.

Wait, the graph: x-axis from 0 to 10, y-axis 0 to 10. Point A is at (2,1), B at (6,3). So the change in y (rise) is 3 - 1 = 2, change in x (run) is 6 - 2 = 4. So slope is rise/run = 2/4 = 1/2. So the numerator (rise) is 2, denominator (run) is 4. So the answer is 2 over 4, so numerator 2, denominator 4.

Answer:

The numerator (rise) is 2, denominator (run) is 4. So slope from A to B is \(\frac{2}{4}\) (or simplified \(\frac{1}{2}\)), but according to the problem's format with a negative sign (which might be an error), but based on the graph, rise is 2, run is 4. So the numerator is 2, denominator is 4.