Which of the following equations represents a line that is parallel to and passes through the point, (3, 4)?

Question

A. y=5x-11

B. y= 5x+19

C. y= -1/5x-4

D. y= 5x-7

Answer 1

(Previous solution has been revised for "parallel lines" requirement).  

It now reads.....

 

Each equation is written in "slope-intercept" form (y=mx+b).  

Recognize that parallel line equations have same slope "m" but

different "y-intercepts".  Substitute the point coordinates

(x=3, y=4) into each equation and check for truth...

 

y=5x-11........Eq A

4=5(3)-11

4=15-11

4=4..............true, Eq A line passes thru given point, any parallel line 

                      must have same slope (m=5).

 

y=5x+19.......Eq B

4=5(3)+19

4=15+19

4=34.............false, line does not pass thru point for Eq B, has

                      same slope, different y-intercept, therefore is parallel.

 

y=-(1/5)x-4...Eq C

4=-(1/5)(3)-4

4=-(3/5)-4

4=-4³/₅.........false, line does not pass thru point for Eq C, slope 

                      is negative reciprocal, Eq C is perpendicular to Eq A.

 

y=5x-7..........Eq D

4=5(3)-7

4=15-7

4=8...............false, line does not pass thru point for Eq D, has 

                      same slope, different y-intercept, therefore is parallel.

 

Summary:  Eq A. y=5x-11 is the equation which passes thru point

(3,4).  Eqs B and D has the same slope as Eq A (m=5), but different

y-intercept (0,b).  So, Eqs B and D satisfy the problem requirements.