Question

Checking Slope-Intercept Form
Step 1: 5 = negative 2 (negative StartFraction 3 Over 10 EndFraction) + b. Step 2: 5 = StartFraction 6 Over 10 EndFraction + b. Step 3: 5 minus StartFraction 6 Over 10 EndFraction = StartFraction 6 Over 10 EndFraction minus StartFraction 6 Over 10 EndFraction + b. Step 4: StartFraction 50 Over 10 EndFraction minus StartFraction 6 Over 10 EndFraction = b. Step 5: StartFraction 44 Over 10 EndFraction = b. Step 6: y = negative 2 x minus 4.4.

A student used the slope-intercept form to write the equation of a line that has a slope of -2 and passes through the point (StartFraction negative 3 Over 10 EndFraction, 5). The student’s work is shown to the left.

Analyze the steps to identify the error.
Step1: student switched the x and y values
Step 3: student needed to add StartFraction 6 Over 10 EndFraction to both sides
Step 5: student subtracted incorrectly
Step 6: student needed to add the b value

Answer 1

The error is in Step 6.

Work is correct through Step 5: substituting y = mx + b gives 5 = -2(-3/10) + b = 6/10 + b, so b = 5 − 6/10 = 50/10 − 6/10 = 44/10 = 4.4. The student then should write y = −2x + 4.4, but wrote y = −2x − 4.4 instead (the sign of b was flipped).