Question

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. \\(\circ\\) step 4 is incorrect because it shows an incorrect substitution of (1, 3) into the point - slope form.

Explanation:

1. Check Step 1: The point \((2, 5)\) – from the graph, when \(x = 2\), \(y\) should be \(5\) (since the line passes through \((2,5)\) as per the grid). So Step 1 is correct.
2. Check Step 2: The point \((1, 3)\) – on the graph, when \(x = 1\), \(y = 3\) (matches the grid). So Step 2 is correct.
3. Check Step 3: Slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using points \((1, 3)\) and \((2, 5)\): \(m=\frac{5 - 3}{2 - 1}=\frac{2}{1}=2\), not \(\frac{1}{2}\). So the slope ratio calculation in Step 3 is wrong.
4. Check Step 4: Point - slope form \(y - y_1=m(x - x_1)\). Substituting \(m = \frac{1}{2}\) (even though slope is wrong) and \((x_1,y_1)=(1,3)\) gives \(y - 3=\frac{1}{2}(x - 1)\), but the error is in Step 3's slope, not Step 4's substitution (given the wrong slope from Step 3).

Answer:

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