Question

find the error tess and jacinta are writing an equation of the line through (3, -2) and (6, 4). is either of them correct? explain your reasoning.
tess
$m = \frac{4 - (-2)}{6 - 3} = \frac{6}{3}$ or 2
$y = mx + b$
$6 = 2(4) + b$
$6 = 8 + b$
$-2 = b$
$y = 2x - 2$
jacinta
$m = \frac{4 - (-2)}{6 - 3} = \frac{6}{3}$ or 2
$y = mx + b$
$-2 = 2(3) + b$
$-2 = 6 + b$
$-8 = b$
$y = 2x - 8$
select choice is correct. select choice switched the x- and y-coordinates on the point that she entered in step select choice.
need help?

Explanation:

Step1: Analyze Tess's Work

Tess used the point \((6, 4)\) but substituted \(x = 4\) and \(y = 6\) (switched \(x\) and \(y\)) in \(y=mx + b\). Correct substitution for \((6, 4)\) should be \(4=2(6)+b\), but she did \(6 = 2(4)+b\), which is wrong.

Step2: Analyze Jacinta's Work

Jacinta used the point \((3, -2)\) and substituted \(x = 3\), \(y=-2\) into \(y=mx + b\) (i.e., \(-2=2(3)+b\)). Solving gives \(b=-8\), so the equation \(y = 2x-8\) is correct. Let's verify with both points:

• For \((3, -2)\): \(y=2(3)-8=6 - 8=-2\) (correct).
• For \((6, 4)\): \(y=2(6)-8=12 - 8 = 4\) (correct).

Jacinta is correct. Tess switched the \(x\)- and \(y\)-coordinates of the point \((6, 4)\) when substituting into \(y = mx + b\) (she used \(x = 4\), \(y = 6\) instead of \(x = 6\), \(y = 4\)). Jacinta correctly used the point \((3, -2)\) for substitution, found \(b=-8\), and the equation \(y = 2x - 8\) satisfies both given points.

Answer:

The first "Select Choice" should be "Jacinta", the second "Select Choice" should be "Tess", and the last "Select Choice" should be the step where Tess substituted (i.e., the step with \(6 = 2(4)+b\), which is her substitution step, so the step number is the one where she plugged in the point, likely the third step of her work or the step with the incorrect substitution). So:

1. Jacinta is correct.
2. Tess switched the \(x\)- and \(y\)-coordinates on the point that she entered in Step (the step where she did \(6 = 2(4)+b\), which is her substitution step for the point \((6, 4)\)).