The equation for line t can be written as y=7/6x-10. line u, which is parallel to line t, includes the point (2,5). which is the equation of line u?

Hi, there--

I am not sure if my answer is going to help you but I am also sure it will, frankly my answer is probaly not what you want but it took some time to write this so I hope this helps!

The Problem:

Consider the line y=7x-6

Find the equation of the line that is parallel to this line and passes through the point (6,-5).

Find the equation of the line that is perpendicular to this line and passes through the point (6,-5).

A Solution:

When two lines are parallel, they have the same slope, but the y-intercepts are different.

{1} parallel line

Your original equation is in slope-intercept form: (y=mx+b). The slope m is the coefficient of the

x term; it's  7.

We know that the parallel line has a slope of 7 and that it passes through the point (6,-5).

We'll substitute these known values into the slope-intercept form and solve for the

y-intercept b.

y = mx + b

-5 = (7)(6) + b

-5 = 42 + b

b = -47

The equation of the parallel line is y = 7x - 47.

{2} perpendicular line

If a line has a slope m, then the line perpendicular to it has the slope -1/m.

Since the original equation has a slope of 7, the perpendicular line has a slope of -1/7.

From here the procedure is quite similar to finding the parallel line's equation. Use the

slope-intercept form to find the y-intercept.

y = mx + b

-5 = (-1/7)(6) + b

-5 = (-6/7) + b

b = -5 + 6/7

b = -29/7

The equation for the perpendicular line is y = (-1/7)x - 29/7.

I hope this helps you!!!