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math help
I have no idea what to do for these questions: HELP!
"Perpendicular to 2x + y = 4 with an x-intercept -1"
What do you do?
And for
"Perpendicular to x + 2y = 8 and has y-intercept 4"
"with x-intercept -1/2 and through (-2,5)"
HELP ME
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We're not supposed to do your homework for you, so here's a different approach.
Right now, your equations are in AX + BY = C form. That means that for the first equation...
A = 2
B = 1
C = 4
So with that knowledge, you can use a shortcut to find the slope of that line. The slope is equal to -A/B. Once you find that, you know that the slope of a line perpendicular to that line is always going to be the opposite reciprocal. So, say that hypothetically the slope of your line is 2. That means that the opposite reciprocal of that line is -1/2, which is the slope of the line perpendicular to that.
Once you've found your perpendicular slope, you can plug it into a y=mx+b equation, along with your x-intercept of -1. (That means that your equation will look like 0=m(-1)+b, except you will put in the slope once you've found it.) At that point, you can solve algebraically to find b. Voila!
I hope I gave you enough information so that you understand the rest of your homework. If you need any more help, feel free to inbox me.
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1. You need to get Y by itself, to turn it into y=mx+b format. So:
2x + y =4
-2x
y=-2x+4
In perpendicular equations, the slope (m) is the opposite reciprocal. The opposite reciprocal of -2 is 1/2
So far we have y=1/2x + ??
You also say that you have the x intercept of -1. "X Intercept" means that it crosses the X axis. For this to happen, the coordinate would have to be (-1,0). Plug that coordinate in for x and y. -1 is x and 0 is y:
0=1/2(-1) + b
Solve:
0=-1/2 + b
+1/2
1/2=b
Plug this into your equation:
y = 1/2x + 1/2
Make sense? It's kind of hard to explain this over the internet, but if you need anymore help you can have my AIM. Anyway, here's the next one:
2. x + 2y = 8
Again, you have to get the y by itself. So start by subtracting the x:
2y = -x + 8
Divide both sides by two so the y is by itself:
y = -1/2x + 4
Now, you say the y intercept is 4. In y=mx+b, b is the y intercept. You already have a four there, so you are good.
3. Remember in #1 when I talked about x intercepts? Same thing here. You have an x intercept of -1/2. X intercept means that it is a point on the s axis. Therefore, the y coordinate can't go up or down. It has to be zero. So your two points are
(-1/2,0) and (-2,5). Remember how to find slope (besides doing rise over run)? The formula is:
Y2-Y1/X2-X1 (Those numbers are subcripts. They should be written in the bottom right corner of the number).
Let's start with the Y's:
5-0=5
And the X's:
-2 - -1/2 = -1 1/2
Don't forget to divide:
5/-1 1/2 = about 3.33. This is your slope (m).
y=3.33x + b
To find b, plug in a coordinate for x and y. It doesn't matter what you pick, but I will choose (-2,5):
5=3.33(-2)+b
5=-6.67 + b
Add 6.67 to both sides to get b by itself:
11.67 = b
Your complete equation is y = 3.33x + 11.67... Don't you just love decimals?
Anyway, I hope this helps you. Let me know if you need anymore.
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