Graph and find the equation of the line in slope intercept form containing Q(5,1) and parallel to line MN with M(-2,4) and N(2,1)

Question

Please help me on this problem. Kind of confused with it. Thank you in advance

Answer 1

The slope of line MN is (4-1)/(-2 -2) = -3/4

 

Parallel lines have the same slope.

 

So the parallel line has slope -3/4 and passes through (5,1)

 

y = m x +  b ----> b = y - mx;

 (5,1)-->  x-5, y=1 and M = -3/4

 

b = 1 - (-3/4)(5) = 1 - (-3/4)(5/1) 

                           = 1 - (-15/4)

                           = 1 + 15/4

                           = 4/4 + 15/4

                            = 19/4

 

The equation of the parallel line is

y = (-3/4)X + 19/4

 

When x=0, y = 19/4. So the y-intercept is (0, 19/4)

 

When x=1, y = (-3/4)(1) + 19/4 = -3/4 + 19/4 = 16/4 = 4

 so (1,4)

 

When x=15, y = -15/4 + 19/4 = 4/4 = 1, so (15,1)

You can now graph the lines .

 

Please verify the slope using "rise over run"

Since the slope is -3/4, that's 3 down and 4 to the right