Question

Analyzing Student Work
Samuel wrote the equation in slope-intercept form using two points of a linear function represented in a table. Analyze the steps Samuel used to write the equation of the line in slope-intercept form.

A 2-column table with 4 rows. Column 1 is labeled x with entries negative 7, negative 5, negative 3, negative 1. Column 2 is labeled y with entries 13, 5, negative 3, negative 11. 1: m = StartFraction negative 3 minus 5 Over (negative 3) minus (negative 5) EndFraction = StartFraction negative 8 Over 2 EndFraction = negative 4. 2: 5 = negative 4 (negative 5) + b. 5 = 20 + b. b = negative 15. 3: y = negative 15 x minus 4.

In which step did Samuel make an error?
In step 1, he substituted the x values for y and the y values for x.
In step 2, he made an arithmetic error.
In step 3, he substituted the wrong values for m and b.
Samuel did not make an error.

Answer 1

In step 3. Steps 1 and 2 are correct (m = (-3−5)/(-3−(−5)) = −8/2 = −4, and using (−5,5) gives 5 = −4(−5)+b ⇒ b = −15). Samuel swapped m and b when writing the final equation. The correct equation is y = −4x − 15 (which checks with the table points).