What is linear manipulation?

Question

I am trying to help a friend with math homework. His teacher is awful, she won't help anyone and is rude. I know from personal experience! Some of the work he was supposed to do was title linear manipulation and writing an equation given to points in a linear function? I haven't done this in quite some time...anyone have any ideas?

Answer 1

Here's 2 examples:

1.) Given point (2,2) and (3,3), find the function.
Step 1: Find the slope.
Slope = rise/run = (y2 - y1) / (x2 - x1)
(3 - 2) / (3 - 2) = 1/1 = 1.

Step 2: Given the slope, find the y intercept by trying to find a point (0, y) that fits the 2 points above, and the slope given.
Use the slope formula: rise / run = 1
(2 - y) / (2 - 0) = 1 = (2 - y) / 2
2 = 2 - y
-y = 0
y = 0
y intercept = 0, 0

Step 3: Once you have the slope, you can write it in slope intercept form:
y = mx + b
m = slope, b = y intercept
y = 1x + 0, or y = x.

2.) (a harder one) Given point (1,4) and (-3, 2), find the function.
Step 1: Find the slope.
m = rise/run = (y2 - y1) / (x2 - x1)
(4 - 2) / (1 - -3) = 2/4 = 1/2 = .5

Step 2: Given the slope, find the y intercept at (0, y)
m = rise / run = 1/2
(4 - y) / (1 - 0) = 1/2 = (4 - y) / 1
4 - y = 1/2
-y = -3.5
y = 3.5
y intercept = 0, 3.5

Step 3: Write it in slope intercept form:
y = mx + b
y = .5x + 3.5

Answer 2

Buddy, everyone gets paid for doing a job right? if he's not doing his job providing his students with enough information. You should report his name, and ask other students in class to be your witness. Then go ask your parents to write a letter to the principle. Everything will be solved. Plus, you must be darn smart in his class to do this. If you're not, ask an intelligent student in your class to help you. Most likely, the bright people will help. No one is different. Trust me on this! it happened to me before.