Question

Terri wrote the equation using slope-intercept form for the line that passes through the points (4, 6) and (–2, 3).

Step 1: m = StartFraction 4 minus (negative 2) Over 6 minus 3 EndFraction = StartFraction 6 Over 3 EndFraction = 2
Step 2: 3 = 2 (negative 2) + b
Step 3: 3 = negative 4 + b. 7 = b.
Step 4: y = 2 x + 7

Which best describes Terri’s first error?
In step 1, the slope of the line should be One-half.
In step 2, she should have substituted the point (4, 6).
In step 3, she should have subtracted 4 from both sides of the equation.
In step 4, the m and b values should be switched.

Answer 1

Terri's first error is in **Step 1**, where she calculates the slope \( m \). The correct formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \( (4, 6) \) and \( (-2, 3) \):

- Let \((x_1, y_1) = (4, 6)\) and \((x_2, y_2) = (-2, 3)\).
- Applying the formula:

\[
m = \frac{3 - 6}{-2 - 4} = \frac{-3}{-6} = \frac{1}{2}
\]

Terri incorrectly calculated the slope as \( 2 \) when the correct slope should be \( \frac{1}{2} \).

Thus, the best description of Terri's first error is: **In step 1, the slope of the line should be One-half.**