The slope of the line is - 3/4
I got my ordered pairs by finding two points on the lines, an noting down their X and Y values.
Then I used the equation Y2 - Y1 (all over) X2 - X1 by plugging in the ordered pairs.
Finally, I solved and got -3/4!
See the attached picture below
Additionally, you can use rise over run, and count the rise and the run. In the image, the rise is three, and the run is four. The slope is negative, which leaves me to know that the answer is -3/4.
Hope this helps :)
The formula of the area of the circle is
Area = pi * (d/2)^2
So using the formula,
Area = 3.14 * (30/2)^2
Area = 3.14 * 15^2
Area = 706.5 ft^2
So the area of the hockey rink is 706.5 ft^2
Well, there are three different ways to solve systems of equations:
a) Graphing
b) Substitution
c) Elimination
Graphing:
If your system of equations are written in slope-intercept form (y=mx+b "m" being the slope and "b" being the y-intercept) its quite easy.
The y-intercept is pretty much where your line touches the y-axis so if your first equation is: y=3x-2 then you will put your first point on (0,-2). Then from that point you follow the slope. if the slope is 3 then you'll rise 3 and run 1 (go three times up and one to the right and put your point right there) till you feel you have enough points to make a line. You do the same process with your second equation.
Substitution:
This is best when you have a system of equations in which an equation tells you what x or y are equal to. For example: if I have "4x+2=y" and "2y+3x= 26" you can "replace" your "2y" with the equation "4x+2=y" which gives you a brand new equation: " 2(4x+2)+3x=26". To solve this you do the distributive property and link like terms which gives you the equation "11x+4=26". Then you solve like a normal equation, isolating x and then you'll get the value of x (in this case x=2). Now you go to the first equation "4x+2=y" and replace "x" to its value (in this case it's 2) and you get y (in this example, y=10).
Elimination:
I think this one is one of the easiest methods. Let's say my systems of equations is "5x-6y=-32" & "3x+6y=48". If you take a look at y's coefficients, you see they are the same. So you can "cancel them out" like this:
5x-6y=-32
+ 3x+6y=48
-----------------------
8x=16 <-------- when you get this, you can solve like a normal equation
x=2
Also, if you have, for example:
2x+6y=190 & 2x+3y=130
You can solve this by: canceling x or multiplying the second equation by 2 and canceling y.
I'm gonna show you how to do the second way (multiplying and canceling y)
My second equation is "2x+3y=130". To get an equivalent equation, I just have to multiply the whole equation by any number. If I want to cancel y, then I have to multiply by 2.
So "2x+3y=130" turns into "4x+6y=260"
Now you follow the same procedure as before:
2x+6y=190
- 4x+6y=260
-------------------------------
-2x= -70
2x=70--------> x=35
Then you pretty much follow the substitution method by replacing "x" to "35" in one of the equations.
Hope this covers all you missed in class. If you have any questions you can comment them here or message me. :D Good luck in your exam!!!
The formula you can use is
y - y1 = m(x - x1)
plug the y value you are given into y1 and the x value you are given into x1. m is for your slope value. after you plug in the known values, solve. your final answer should be in standard form which is
Ax + By = C
your answer should not contain any fractions and your Ax value cannot be a negative value, By and C can be negative though.
hope this helps :)
3a+b+a+b = (3a+a) + (b+b) = 4a + 2b
