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 equation \(y - 3=-(x + 1)\) can be rewritten in slope - intercept form \(y=mx + b\) (where \(m\) is the slope and \(b\) is the \(y\) - intercept).

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The slope \(m=-1\). Parallel lines have the same slope.

Step2: Check Trish's line

Trish's line is \(y - 2=-1(x - 4)\). Rewrite it in slope - intercept form:

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Slope \(m=-1\), and when \(x = 4\), \(y=-4 + 6=2\). So it passes through \((4,2)\)

Step3: Check Demetri's line

Demetri's line is \(y=-x + 6\). Slope \(m=-1\). But when \(x = 4\), \(y=-4+6 = 2\). It also passes through \((4,2)\)

Answer:

Both students are correct; the slope should be \(-1\), and the line passes through \((4,2)\) with a \(y\) - intercept of \(6\).