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

Let's analyze Jolon’s work step by step:

1. **Step 1**: \(-2 = 3(5) + b\)
This step is correct. He substituted the point (5, -2) into the equation \(y = mx + b\).

2. **Step 2**: \(-2 = 15 + b\)
This is also correct, as \(3(5) = 15\).

3. **Step 3**: \(-2 + 15 = 15 + 15 + b\)
This is where Jolon made an error. The correct equation should be:
\(-2 - 15 = b\) (not adding 15 to both sides).

The correct next step would be \( -2 - 15 = b \). Thus, \( b = -17 \).

4. **Step 4**: \(-13 = b\)
This is incorrect because, as established in the previous step, he should have found \(b = -17\).

5. **Step 5**: \(y = 3x - 13\)
This step is incorrect because the value of \(b\) is wrong based on the error made in Step 4. The correct equation should be \(y = 3x - 17\).

The error Jolon made was in **Step 3**, where he incorrectly combined the terms. Therefore, the correct answer is:

**He added 15 to both sides in step 3.**