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.

To determine which student, if any, is correct, we need to find the equation of the line that is parallel to and passes through .First, let's find the slope of the given line . We can rewrite it in slope-intercept form where is the slope and is the y-intercept. So, the slope of the given line is .Since parallel lines have the same slope, the slope of the line we are looking for is also .Now, let's use the point-slope form of a line, which is , where is a point on the line and is the slope.Using the point and the slope , we have: This is Trish's equation, so Trish is correct.Now, let's check Demetri's equation . To see if it is the same as Trish's equation, we can rewrite it in point-slope form: Comparing this with Trish's equation , we can see that they are not the same. Therefore, Demetri is not correct.In conclusion, Trish is the only student who is correct; the slope should be and the line passes through .