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 . Step 4: Substitute those values into the point-slope form. y – y1 = m(x – x1) y – 3 = (x – 1) Which of Talia’s 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.

Answer 1

Given that aim of Talia is to write the equation in point slope, she will be required to use the point slope form given by:
m(x-x1)=y-y1
where:
m is the slope of the equation given by:
m=(y-y1)/(x-x1)
that means to calculate for m we will need at least 2 points.

From the steps given, she made a mistake in the 4th step. It was wrong substitution. Hence the answer is:
Step 4 is incorrect because it shows an incorrect substitution of (1, 3) into the point-slope form.