Answer:
C. [tex]\frac{1}{2}[/tex]
Skills needed: Slope Formula
Step-by-step explanation:1
1) The slope is an important concept in algebra, and is also known as the rate of change, or growth rate.
- When graphing a linear equation, the slope determines how steep the line is. Slope can also be negative.
- To find slope, there is a formula you can use. In order to use the formula, you need to be given 2 coordinate points.
- This formula is not that hard to use, and should be remembered as it is a pretty important formula.
------------------------------------------------------------------------------------------------------------- 2) The formula for slope is:
Given two coordinate pairs: [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]
The formula is:
---> [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] also known as [tex]\frac{\triangle y}{\triangle x}[/tex] (change of y over the change of x)
Let's use this formula for this problem (since we are given two coordinate points)
---> [tex](-9, 6)[/tex] is the first point, [tex](-3, 9)[/tex] is the second point
- [tex]-9[/tex] is [tex]x_1[/tex]
- [tex]6 [/tex] is [tex]y_1[/tex]
- [tex]-3[/tex] is [tex]x_2[/tex]
- [tex]9[/tex] is [tex]y_2[/tex]
Let's plug it in below:
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{9-6}{-3-(-9)} [/tex]
[tex]-3-(-9)[/tex] can be made into [tex]-3+9[/tex] since subtracting by a negative number is the same as adding a positive
[tex]9-6 = 3[/tex]
[tex]-3+9=6[/tex]
---> [tex]\frac{9-6}{-3-(-9)}=\frac{3}{6} = \frac{1}{2}[/tex]
In most simplified form, it should be one-half, which is answer choice C.
