Ageometry 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.

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

Step-by-step explanation:

Two equations are parallel when they have the same slope. Given the function:

y – 3 = −(x + 1)

It has the form (called point-slope form): y - y0 = m*(x -x0)

where (x0,y0) is a point that correspond to the line and m is the slope,  so the its slope is -1.

Then the equation:

y - 2 = -(x - 4)

is parallel to the original and passes through (4, 2). So, Trish is correct.

Another way to express the equation of a line is the slope-intercept form:

y = m*x + b

where b is the y-intercept of the equation. The slope has to be -1 and the equation has to passes through (4, 2),  then:

2 = (-1)*4 + b

2 + 4 = b

b = 6

Therefore, the equation y = -x + 6 satisfy the requirements, and Demetri was also correct.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

the answer is d (-2, -4); 6. hope you got it down : d