step 1: choose a point on the line, such as (2, 5).
step 2: choose another point on the line, such as (1, 3).
step 3: count units to determine the slope ratio. the line runs 1 unit to the right and rises 2 units up, so the slope is $\frac{1}{2}$.
step 4: substitute those values into the point - slope form.
$y - y_1 = m(x - x_1)$
$y - 3 = \frac{1}{2}(x - 1)$
which of talia’s steps is incorrect?
step 3 is incorrect because it shows an incorrect ratio for the slope.
step 2 is incorrect because it uses a point that is not on the line.
step 1 is incorrect because it uses a point that is not on the line.
step 4 is incorrect because it shows an incorrect substitution of (1, 3) into the point - slope form.

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# Brief Explanations:
1. First, check the points $(2,5)$ and $(1,3)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using $(2,5)$ as $(x_2,y_2)$ and $(1,3)$ as $(x_1,y_1)$, we get $m=\frac{5 - 3}{2 - 1}=\frac{2}{1} = 2$, not $\frac{1}{2}$. So Step 3 has an incorrect slope ratio.
2. Check Step 2: The point $(1,3)$ - let's see the line. From $(2,5)$, if we go left 1 (x - 1) and down 2 (y - 2), we get $(1,3)$, so $(1,3)$ is on the line. So Step 2 is correct.
3. Check Step 1: The point $(2,5)$ - looking at the graph (the line passes through it), so Step 1 is correct.
4. Check Step 4: The point - slope form is $y - y_1=m(x - x_1)$. Using $(1,3)$ as $(x_1,y_1)$ and $m = \frac{1}{2}$ (even though slope is wrong, substitution is correct for the given $m$). But the error is in Step 3's slope calculation. Wait, no - wait, the slope between $(2,5)$ and $(1,3)$ is $\frac{5 - 3}{2 - 1}=2$, so Step 3 says slope is $\frac{1}{2}$, which is wrong. But also, let's check the options again. Wait, the option "Step 2 is incorrect..." - no, $(1,3)$ is on the line. Wait, maybe I made a mistake. Wait, the line in the graph: let's see the y - intercept. The line passes through (0,1) maybe? Wait, from (2,5), slope 2: $y - 5 = 2(x - 2)$ → $y=2x + 1$. So when x = 1, y = 3. So (1,3) is on the line. When x = 2, y = 5, so (2,5) is on the line. Then the slope between (2,5) and (1,3) is $\frac{5 - 3}{2 - 1}=2$, so Step 3 says slope is $\frac{1}{2}$, which is incorrect. But wait, the option "Step 2 is incorrect because it uses a point that is not on the line" - no, (1,3) is on the line. Wait, maybe the graph is different. Wait, the user's graph: the line has a positive slope, passes through (0,1) maybe? Let's recalculate. If the line passes through (2,5) and (0,1), then slope is $\frac{5 - 1}{2 - 0}=\frac{4}{2}=2$. So from (2,5) to (1,3): x decreases by 1, y decreases by 2? Wait no, 5 - 3 = 2, 2 - 1 = 1. So it's a rise of - 2 (or fall of 2) for a run of - 1 (or left 1). So slope is $\frac{2}{1}=2$ (since slope is rise over run, and both change in y and change in x: $\Delta y=3 - 5=-2$, $\Delta x=1 - 2=-1$, so $\frac{-2}{-1}=2$). So Step 3 says slope is $\frac{1}{2}$, which is wrong. But the option "Step 2 is incorrect..." - no, (1,3) is on the line. Wait, maybe I misread the points. Wait, the first point is (2,5), second is (1,3). Let's plot them: (2,5) is 2 right, 5 up. (1,3) is 1 right, 3 up. The difference in x: 2 - 1 = 1 (run is 1, right), difference in y: 5 - 3 = 2 (rise is 2, up). So slope is rise over run = 2/1 = 2. So Step 3 says slope is 1/2, which is incorrect. But the option "Step 2 is incorrect..." - no, (1,3) is on the line. Wait, maybe the graph is such that (1,3) is not on the line? Wait, the problem says "such as (1,3)" - maybe the line in the graph doesn't pass through (1,3). Wait, the user's graph: the line has a y - intercept at (0,1) maybe? Let's check with (2,5): slope from (0,1) to (2,5) is (5 - 1)/(2 - 0)=4/2 = 2. So (1,3) is on the line (since 1*2 + 1 = 3). So (1,3) is on the line. So Step 2 is correct. Step 1: (2,5) is on the line (2*2 + 1 = 5), so correct. Step 4: substitution is correct for the given m. So the incorrect step is Step 3, but wait, the option "Step 2 is incorrect..." - no, maybe I made a mistake. Wait, the options:

Option 1: Step 3 is incorrect because it shows an incorrect ratio for the slope.

Option 2: Step 2 is incorrect because it uses a point that is not on the line.

Option 3: Step 1 is incorrect because it uses a point that is not on the line.

Option 4: Step 4 is incorrect because it shows an incorrect substitution.

Wait, let's re - evaluate. Let's take the two points (2,5) and (1,3). The slope is (5 - 3)/(2 - 1)=2/1 = 2. So Step 3 says slope is 1/2, which is wrong. So Option 1 says Step 3 is incorrect because of slope ratio - that's correct. But wait, maybe the line in the graph is different. Wait, maybe (1,3) is not on the line. Let's see: if the line passes through (2,5) and (0,1), then when x = 1, y = 1+2*1 = 3. So (1,3) is on the line. So Step 2 is correct. So the incorrect step is Step 3, but wait, the option "Step 2 is incorrect..." - no, that's wrong. Wait, maybe I messed up. Wait, the problem is which step is incorrect. Let's check each option:

- Step 3: slope calculation. Between (2,5) and (1,3), slope is 2, so Step 3 says 1/2 - incorrect. So Option 1 is correct? But wait, the other option: Step 2 is incorrect. Wait, maybe the line in the graph doesn't pass through (1,3). Let's assume the graph: the line goes through (2,5) and (0,1), so (1,3) is on the line. So Step 2 is correct. Step 1: (2,5) is on the line - correct. Step 4: substitution is correct (for the given m). So the incorrect step is Step 3, so Option 1 is correct. But wait, the option "Step 2 is incorrect..." - no, (1,3) is on the line. So the correct answer is the first option: "Step 3 is incorrect because it shows an incorrect ratio for the slope." Wait, but wait, maybe I made a mistake in slope direction. Wait, from (1,3) to (2,5): run is 1 (right), rise is 2 (up), so slope is 2/1 = 2. So Step 3 says slope is 1/2, which is wrong. So Step 3 is incorrect. So the answer is the first option.
# Answer:
Step 3 is incorrect because it shows an incorrect ratio for the slope.

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