Question

Examining Student Work
Step 1: y minus (negative 2) = three-fourths (x minus 3). Step 2: y + 2 = three-fourths x minus StartFraction 9 Over 4 EndFraction. Step 3: y + 2 + 2 = three-fourths x minus StartFraction 9 Over 4 EndFraction + StartFraction 8 Over 4 EndFraction. Step 4: y = three-fourths x minus one-fourth.

A student used the point-slope form to write the equation of a line that has a slope of Three-fourths and passes through the point (3, –2). The student’s work is shown to the left.


Examine the steps to determine whether the student made an error.

The student made
an error in Step 4
.

Answer 1

Steps 1 and 2 are correct:
y - (−2) = (3/4)(x − 3) → y + 2 = (3/4)x − 9/4.

The mistake occurs in Step 3 (so Step 4’s result is wrong). From y + 2 = (3/4)x − 9/4 you should subtract 2 from both sides, not add 2. Correctly:
y = (3/4)x − 9/4 − 2 = (3/4)x − 9/4 − 8/4 = (3/4)x − 17/4.

So the final equation is y = (3/4)x − 17/4.