Jolon used the slope-intercept form to write the equation of a line with slope 3 that passes through the point (5, –2). His work is shown below.

Question

Step 1: Negative 2 = 3 (5) + b
Step 2: negative 2 = 15 + b
Step 3: Negative 2 + 15 = 15 + 15 + b
Step 4: Negative 13 = b
Step 5: y = 3x – 13

Analyze the steps. In which step did the Jolon make an error?
He switched the x- and y- values in step 1.
He multiplied incorrectly in step 2.
He added 15 to both sides in step 3.
He forgot to add the b-value in step 5.

Answer 1

To analyze Jolon’s steps, let’s review the work he did for writing the equation in slope-intercept form (y = mx + b):

1. Step 1: \(-2 = 3(5) + b\)

   • This step correctly substitutes \(x = 5\) and \(y = -2\) into the equation using the correct slope \(m = 3\).

2. Step 2: \(-2 = 15 + b\)

   • Here, Jolon correctly calculated \(3(5) = 15\).

3. Step 3: \(-2 + 15 = 15 + b\)

   • In this step, he seems to have added \(15\) to both sides incorrectly. It should actually be \(-2 - 15 = b\) instead of trying to balance both sides that way.

4. Step 4: \(-13 = b\)

   • This step is incorrect because he didn’t perform the right operation in the previous step. The correct operation should be \(-2 - 15 = -17\).

5. Step 5: \(y = 3x - 13\)

   • He wrote the final equation with the incorrect \(b\) value.

Based on this analysis, Jolon made an error in Step 3, where he incorrectly tried to add 15 to both sides instead of subtracting 15 from -2 to find \(b\). Thus, the correct option is:

He added 15 to both sides in step 3.