A calling card offers two methods of paying for a phone call. Method A charges $0.02 per minute but has a $0.6 connection fee. Method B charges $0.045 per minute but has no connection fee. Write the equations that show the total cost, y, of a call of x minutes for methods A and B and determine their intersection point. What does the intersection point represent?

The equation representing Method A is y =

Well, if I were a calling card, I'd probably have a gimmick too. Let's chat about Method A, shall we?

For Method A, the total cost, y, of a call of x minutes can be calculated using the equation:

y = 0.02x + 0.6

This equation takes into account the connection fee of $0.6 and the $0.02 per minute charge.

Now, let's take a look at Method B. Brace yourself, because there's no connection fee here, but the per minute charge is slightly higher.

For Method B, the total cost, y, of a call of x minutes is given by:

y = 0.045x

This equation only considers the per minute charge of $0.045.

To find the intersection point, we set the two equations equal to each other:

0.02x + 0.6 = 0.045x

Now let's solve for x:

0.02x - 0.045x = -0.6

-0.025x = -0.6

x = -0.6 / -0.025

x = 24

Hooray! The intersection point is x = 24. So when a call lasts for 24 minutes, the costs for both Method A and Method B are the same.

But what does this intersection point represent, you ask? Well, it's the magical moment when both methods offer the same cost for a call. You can think of it as the tipping point where it becomes more economical to choose one method over the other, depending on the duration of the call.

Hope that clears things up for you!

0.02x + 0.6

The equation representing Method B is y = 0.045x

To determine the intersection point, we need to find the values of x and y where the two equations are equal:

0.02x + 0.6 = 0.045x

Simplifying the equation:

0.6 = 0.045x - 0.02x

0.6 = 0.025x

Dividing both sides by 0.025:

x = 0.6 / 0.025

x = 24

Now we can substitute the value of x back into one of the equations to find the corresponding value of y. Let's use the equation for Method A:

y = 0.02(24) + 0.6

y = 0.48 + 0.6

y = 1.08

Therefore, the intersection point is (24, 1.08).

The intersection point represents the number of minutes (x) and the cost (y) at which Method A and Method B have the same total cost for a phone call. In this case, it means that a call lasting 24 minutes using Method A and a call lasting 24 minutes using Method B will have the same total cost of $1.08.

To find the equation that represents Method A, we need to consider two components: the per-minute charge and the connection fee.

The per-minute charge for Method A is $0.02 per minute. So, the cost of the call for x minutes based on the per-minute charge alone will be 0.02x.

In addition to the per-minute charge, Method A also has a $0.6 connection fee. This connection fee is charged regardless of the length of the call. Therefore, the total cost, y, of a call of x minutes for Method A is given by the equation:

y = 0.02x + 0.6

Now let's find the equation that represents Method B. Method B only has a per-minute charge, so the total cost, y, of a call of x minutes for Method B is simply:

y = 0.045x

To find the intersection point of these two methods, we need to equate their total costs:

0.02x + 0.6 = 0.045x

Now we can solve this equation to find the value of x at the intersection point.

0.02x - 0.045x = -0.6

-0.025x = -0.6

Dividing both sides of the equation by -0.025:

x = -0.6 / -0.025

x = 24

So, the intersection point is x = 24. To find the corresponding y-value, we can substitute this value back into either equation. Let's use Method A's equation:

y = 0.02x + 0.6
y = 0.02 * 24 + 0.6
y = 0.48 + 0.6
y = 1.08

Therefore, the intersection point is (24, 1.08).

The intersection point represents the number of minutes (x) and the total cost (y) at which both methods A and B will have the same cost. In other words, it is the point at which it becomes more cost-effective to use one method over the other.

A: y = .60 + .02x

B: y = .045x

I guess you can take it from there, eh?