Line %0D%0Ap%0D%0A%0D%0A represents the equation %0D%0Ay%0D%0A=%0D%0A5%0D%0A2%0D%0Ax%0D%0A−%0D%0A10%0D%0A.%0D%0A%0D%0A=%0D%0A5%0D%0A2%0D%0A%0D%0A-%0D%0A10%0D%0A.%0D%0A In the standard %0D%0A(%0D%0Ax%0D%0A,%0D%0A %0D%0Ay%0D%0A)%0D%0A(%0D%0A%0D%0A,%0D%0A %0D%0A%0D%0A)%0D%0A coordinate plane, line %0D%0Aq%0D%0A%0D%0A is parallel to line %0D%0Ap%0D%0A%0D%0A and passes through %0D%0A(%0D%0A4%0D%0A,%0D%0A1%0D%0A)%0D%0A(%0D%0A4%0D%0A,%0D%0A1%0D%0A)%0D%0A. Which of the following equations is represented by line %0D%0Aq%0D%0A%0D%0A ?%0D%0A%0D%0A%09A.%09%0D%0Ay%0D%0A=%0D%0A−%0D%0A5%0D%0A2%0D%0Ax%0D%0A−%0D%0A9%0D%0A%0D%0A=%0D%0A-%0D%0A5%0D%0A2%0D%0A%0D%0A-%0D%0A9%0D%0A%0D%0A%09B.%09%0D%0Ay%0D%0A=%0D%0A−%0D%0A2%0D%0A5%0D%0Ax%0D%0A−%0D%0A3%0D%0A5%0D%0A%0D%0A=%0D%0A-%0D%0A2%0D%0A5%0D%0A%0D%0A-%0D%0A3%0D%0A5%0D%0A%0D%0A%09C.%09%0D%0Ay%0D%0A=%0D%0A2%0D%0A5%0D%0Ax%0D%0A+%0D%0A3%0D%0A5%0D%0A%0D%0A=%0D%0A2%0D%0A5%0D%0A%0D%0A+%0D%0A3%0D%0A5%0D%0A%0D%0A%09D.%09%0D%0Ay%0D%0A=%0D%0A5%0D%0A2%0D%0Ax%0D%0A+%0D%0A9%0D%0A%0D%0A=%0D%0A5%0D%0A2%0D%0A%0D%0A+%0D%0A9%0D%0A%0D%0A%09E.%09%0D%0Ay%0D%0A=%0D%0A5%0D%0A2%0D%0Ax%0D%0A−%0D%0A9
To find the equation represented by line q, which is parallel to line p and passes through (4,1), we know that the slope of line q will be the same as the slope of line p.
The slope of line p is 5/2.
To find the equation of line q, we can use the point-slope form:
y - y1 = m(x - x1),
where (x1, y1) is the point (4,1) on line q and m is the slope, which is 5/2.
Plugging in the values:
y - 1 = 5/2(x - 4).
Expanding and simplifying:
y - 1 = 5/2x - 10.
Adding 1 to both sides:
y = 5/2x - 9.
Therefore, the equation represented by line q is:
y = 5/2x - 9.
So, the correct equation is:
A. y = -5/2x - 9