Question

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.

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.**