Question

What is the equation of a line in general form that does not have a y-intercept and goes through the point (3,6) ?

(** I know the answer is x-3 = 0, please EXPLAIN)

Answer 1

Answer:

$x = 3$

Step-by-step explanation:

Step 1:  Determine the equation

So we know that our equation does not have a y-intercept which means that it doesn't intersect ANYWHERE on the y-axis.  Therefore, this means that our equation will be a straight vertical line that doesn't move side to side and just goes straight up and down.  We also know that our point is (3, 6) which means that our x-value will be 3 and this is where the equation will be located.  

There are several ways to display our answer where x = 3 is the most common way which basically means give me all of the y-values for the same x value of 3.  Another way of saying it is x - 3 = 0 which either way when adding 3 to both sides gives you x = 3 which is what I usually go with.

Answer: $x = 3$

Answer 2

Answer:

x = 3 or x - 3 = 0

Step-by-step explanation:

Given

• It does not have a y-intercept
• Passes through the point (3, 6)

Solving

• If the line cannot touch the y-axis, it has to be parallel to it (in other words, the line must be vertical)
• Since the x-value is constant for a vertical line and it passes through the point (3, 6), the equation of the line will be :
• x = 3 or x - 3 = 0