Question

The square PQRS has vertices P(–8, 4), Q(–5, 4), R(–5, 1), and S(–8, 1). A student determined that the equation of the line QS is y=-1+9. Evaluate the student’s response. A. The student calculated the equation correctly. B. The student calculated the y-intercept correctly but did not calculate the slope correctly. C. The student calculated the slope correctly but did not calculate the y-intercept correctly. D. The student calculated neither the slope nor y-intercept correctly.

Answer 1

The correct question is
The square PQRS has vertices P(–8, 4), Q(–5, 4), R(–5, 1), and S(–8, 1). A student determined that the equation of the line QS is y=-1x+9. Evaluate the student’s response


we know that
The square PQRS has vertices P(–8, 4), Q(–5, 4), R(–5, 1), and S(–8, 1)

step 1
find the slope m of the line QS
m=(y2-y1)/(x2-x1)-----> m=(1-4)/(-8+5)---> m=-3/-3----> m=1

step 2
with m=1 and point Q(–5, 4)
find the equation of the line QS
y-y1=m*(x-x1)------> y-4=1*(x+5)----> y=x+5+4----> y=x+9

therefore
the student had the slope incorrect
The student calculated the y-intercept correctly

the answer is the option
B. The student calculated the y-intercept correctly but did not calculate the slope correctly.