Of the following linear equations, which pass(es) through the origin?

Question

Of the following linear equations, which pass(es) through the origin?

1. y=(2/3)x+1

2. y=-0.1x+6

3. 2x-3y=6

4. y=x

5. y=-5x+4

6. 6x+3y=9

7. y=3x-5

 

 

Please explain how to solve. Thanks!

Answer 1

The origin is point (0,0).

 

When x=0, the x-term (for example, 5x) is 0.  That means any constant (for example, the b in y=mx + b) must be 0 (may be missing).

 

You may look at the equations very quickly to determine which lines go through (0,0); you do not need to find the value of y when x=0.

Answer 2

Nick, use the coordinates of the origin to see which equation is true.

Answer 3

Nick,

 

This is a very simple question and you really do not even need to solve anything.

 

Remember that in the equation y = mx +c        m is the slope and c is the y-intercept (or the value at which the line intercepts the y axis)

 

Since you have been given that the line passes through the origin (0,0), it entails that the y intercept must be 0.

 

Of the 7 equations provided only no. 4 has an y intercept of 0 for y=x can be re-written as y=1x + 0.

 

Hence equation 4 is the answer.