Question

talia wants to write the equation of the graphed line in point - slope form. these are the steps she plans to use:
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 talias steps is incorrect?
\\(\circ\\) step 1 is incorrect because it uses a point that is not on the line.
\\(\circ\\) step 2 is incorrect because it uses a point that is not on the line.
\\(\circ\\) step 3 is incorrect because it shows an incorrect ratio for the slope.

Explanation:

Step1: Analyze Step 1

Check if (2,5) is on the line. From the graph, when x=2, y should be 5? Wait, let's check the slope. Wait, let's calculate slope between (1,3) and (2,5)? Wait, no, let's check the graph. Wait, the line passes through (0,1)? Wait, no, looking at the grid, let's take two points. Let's see, when x=1, y=3? Wait, no, maybe the points are (1,3) and (2,5)? Wait, no, let's calculate slope correctly. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take (1,3) and (2,5): $m=\frac{5 - 3}{2 - 1}=\frac{2}{1}=2$. Wait, Talia said slope is $\frac{1}{2}$, which is wrong. Wait, but first, check the points. Wait, Step 1: (2,5) – is that on the line? Let's see the graph. The line goes through, say, (0,1), (1,3), (2,5)? Wait, (1,3): when x=1, y=3? Let's check the grid. The y-axis: each grid is 1 unit. So (1,3) is on the line, (2,5) is on the line. Wait, but when calculating slope, from (1,3) to (2,5), run is 1, rise is 2? Wait, no, rise is 5 - 3 = 2, run is 2 - 1 = 1, so slope should be 2, not $\frac{1}{2}$. So Step 3 has incorrect slope ratio. Wait, let's check the options. The options are: Step1 (point not on line), Step2 (point not on line), Step3 (incorrect slope ratio). Let's check Step1: (2,5) – is that on the line? From the graph, when x=2, y=5? Let's see the line: at x=0, y=1? Wait, no, maybe the line passes through (0,1), (1,3), (2,5). So (2,5) is on the line, (1,3) is on the line. So Step1 and Step2 points are on the line. Then Step3: slope calculation. The line runs 1 unit right (from x=1 to x=2) and rises 2 units (from y=3 to y=5), so slope is $\frac{rise}{run}=\frac{2}{1}=2$, but Talia said $\frac{1}{2}$, which is incorrect. So Step3 is incorrect.

Step2: Confirm other steps

Step1: (2,5) is on the line (since (1,3) and (2,5) are on the line, as slope 2). Step2: (1,3) is on the line. So Step3 has incorrect slope ratio.

Answer:

Step 3 is incorrect because it shows an incorrect ratio for the slope. (The option: "Step 3 is incorrect because it shows an incorrect ratio for the slope.")