# Graphs

Graphs are actually a fairly new form of mathematical analysis, first systematically investigated in the 1930s. This link has a short and, hopefully, informative article on the history of graphs.

## 4/3 Graphs

Always take the time to carefully read the question, identify the bottom line, and assess your options. Then attack the problem and loop back to check your answer. Only after that should you look at the answer choices to select the correct one.

In the figure, the slope of the line through points P and Q is $\frac{3}{2}$. What is the value of k?

First, note the bottom line at the top of your scratch work.

k = ?

Next, assess your options. Getting from a slope to one part of a coordinate pair may take a few steps, so in this case the best way to start is to simply begin with what you know and move toward what you want.

You know that slope is rise over run, and you can calculate the total rise since you have both of the y coordinates for the two points. Using this information, you can set up a proportion.

7 - 1 = 6

$\frac{rise}{run}=\frac{3}{2}=\frac{6}{x}$

From here, you can either cross-multiply and solve for x or use multiples to determine its value (2*3=6, so 3*3=x). Either way, x = 4.

Now that you have solved for x, loop back to the bottom line to see if you are finished.

k = ?

You found the difference between the two x-values, but not the value of k. There is still one step left! Since x, the difference between the x coordinates of P and Q, is 4, simply add the value of the first x coordinate to find the value of k.

4 + 1 = 5

Now look at the answer choices

A) 4

B) 5

C) 6

D) 7

E) 8