# SAT Math : How to find the solution to an equation

## Example Questions

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### Example Question #101 : Linear / Rational / Variable Equations

Calculate the slope of the line.

Explanation:

In order to solve for the slope, we need to recall how to find the slope of a line. , where  are points on the line.

So we will pick , and .

### Example Question #102 : Linear / Rational / Variable Equations

What equation best represents the following table?

Explanation:

The first step is to find the common ratio amongst the data.

We can that the common ratio is .

Now we need to set up an equation that will give an answer for any time.

We can set up an exponential decay model, the general equation is,

, where  is the starting amount,  is the common ratio and  is time.

After plugging our numbers in, we get

### Example Question #145 : Algebra

Sally sells custom picture frames.  Her monthly fixed costs are $350. It costs$10 to make each frame.  Sally sells her picture frames for \$35 each.

How many picture frames must Sally sell in order to break even?

Explanation:

The break-even point is where the costs equal the revenues.

Let  = # of frames sold

Costs:

Revenues:

Thus,

So 14 picture frames must be sold each month to break-even.

### Example Question #103 : Linear / Rational / Variable Equations

8 is 3 greater than the square root of an unknown number. What is the unknown number?

Explanation:

In order to solve for the unknown number, you must write an equation and solve for a variable. 8 is 3 greater than the square root of an unknown number translates to

To solve for a you must subtract 3 from both sides, and then square both sides.

As you can see,

and

So, the value of the unknown number is 25.

Solve