Question

a geometry class is asked to find the equation of a line that is parallel to y - 3 = -(x + 1) and passes through (4, 2). trish states that the parallel line is y - 2 = -1(x - 4). demetri states that the parallel line is y = -x + 6. are the students correct? explain. trish is the only student who is correct; the slope should be -1, and the line passes through (4, 2). demetri is the only student who is correct; the slope should be -1, and the y - intercept is 6. both students are correct; the slope should be -1, passing through (4, 2) with a y - intercept of 6. neither student is correct; the slope of the parallel line should be 1.

Explanation:

Step1: Find the slope of the given line

The given line is $y - 3=-(x + 1)$ which can be rewritten in point - slope form $y - y_1=m(x - x_1)$. Here, the slope $m=-1$. Parallel lines have equal slopes.

Step2: Check Trish's equation

Trish's equation is $y - 2=-1(x - 4)$ which is in point - slope form $y - y_1=m(x - x_1)$ with $m=-1$ and the point $(x_1,y_1)=(4,2)$. This is a correct equation for a line with slope $-1$ passing through $(4,2)$.

Step3: Check Demetri's equation

Demetri's equation is $y=-x + 6$ which is in slope - intercept form $y=mx + b$ with $m=-1$ and $b = 6$. Substitute $x = 4$ into $y=-x + 6$, we get $y=-4 + 6=2$. So the line $y=-x + 6$ also passes through the point $(4,2)$.

Answer:

C. Both students are correct; the slope should be $- 1$, passing through $(4,2)$ with a $y$-intercept of $6$.