Find the value of k

Question

The lines of linear functions y=2x+3 and x-3y=k intersect on the x-axis. Find the value of consonant k.

Answer 1

y = 2x + 3 ⇒ x-intercept is (-3/2, 0)

For the second line to intersect at the same point, this pair must solve the second equation.

-3/2 - 3(0) = k

Answer 2

Write the second equation in slope-intersect form.

 

-3y = -x + k

 

   y = (1/3)x - (1/3)k

 

 

Both equations will have y=0.   Use this fact to solve for x.

 

0 = 2x + 3              and                 0 = (1/3)x - (1/3)k

 

-3 = 2x                                          -(1/3)x = -(1/3)k

 

-3/2 = x                                              x = k

 

 

The two equations must have the same x value as well.

 

-3/2 = k

Answer 3

Hi Rock,

 

If the two lines intersect on the x-axis, then the y-coordinate at that point is 0.

 

Therefore,

y = 2x + 3

0 = 2x + 3

 

For the second equation, put 0 in for y and

x - 3y = k

x - 3(0) = k

x - 0 = k

x = k

 

x and k are the same!  Go back to 

0 = 2x + 3 and put in k

0 = 2k + 3

-3 =2k

-3/2 = k

 

Hope this helps!

JMJ