Linear Equations: Finding Lines with Positive Values in All Domains

Which equation represents a line that is positive in domain for each value of x.

To find out if the equation intersects the x-axis, we need to substitute y=0 in each equation.
If the function has a solution where y=0 then the equation has an intersection point and is not the correct answer.

Let's start with the first equation:

y = 3x+8

We will substitute as instructed:

0 = 3x+8

3x = -8

x = -8/3

Although the result here is not a "nice" number, we see that we are able to arrive at a result and therefore this answer is rejected.

Let's move on to the second equation:

y = 300x+50

Here too we will substitute:

0 = 300x + 50
-50 = 300x

-50/300 = x
-1/6 = x

In this exercise too we managed to arrive at a result and therefore the answer is rejected.

Let's move on to answer C:

y = 3

We will substitute:

0 = 3

We see that here an impossible result is obtained because 0 can never be equal to 3.

Therefore, we understand that the equation in answer C is the one that does not intersect the x-axis, and is in fact positive all the time.

Therefore answer D is also rejected, and only answer C is correct.