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?
step 1 is incorrect because it uses a point that is not on the line.
step 2 is incorrect because it uses a point that is not on the line.
step 3 is incorrect because it shows an incorrect ratio for the slope.
step 4 is incorrect because it shows an incorrect substitution of (1, 3) into the point-slope form.

Explanation:

Step1: Verify Step 1 point

Check if (2,5) is on the line: For the line, when $x=2$, $y$ should equal $2*2+1=5$, so (2,5) is valid.

Step2: Verify Step 2 point

Check if (1,3) is on the line: When $x=1$, $y=2*1+1=3$, so (1,3) is valid.

Step3: Calculate correct slope

Slope $m=\frac{y_2-y_1}{x_2-x_1}=\frac{5-3}{2-1}=2$. The stated slope $\frac{1}{2}$ is wrong.

Step4: Verify Step 4 substitution

Point-slope form with $(x_1,y_1)=(1,3)$ and $m=\frac{1}{2}$ is $y-3=\frac{1}{2}(x-1)$, substitution is correct (but slope is wrong from Step3).

Answer:

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