SOLUTION: I have one question that has three parts to it part A , Part B, and Part C part a is Can you give me your definition of Linear Equations? Part B is there a formula for linear

Algebra ->  Linear-equations -> SOLUTION: I have one question that has three parts to it part A , Part B, and Part C part a is Can you give me your definition of Linear Equations? Part B is there a formula for linear       Log On


   



Question 1011791: I have one question that has three parts to it part A , Part B, and Part C
part a is Can you give me your definition of Linear Equations?
Part B is there a formula for linear equations?
Part C is how can i memorize how to solve for linear equations using statement and reason.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
part a: An equation that makes a straight line when it is graphed.
Often written in the form: y+=+mx%2Bb
what it means:
y+= how far up
x = how far along
m = Slope or Gradient (how steep the line is)
b = the y-intercept (where the line crosses the y axis)
How do you find "m" and "b"?

b is easy: just see where the line crosses the y axis and you do it by setting x=0+ in given equation and solving for y
+m (the Slope) needs some calculation:
+m=%28change_in_y%29%2F%28change_in_x%29 which means if you are given two points that lie on a line and their coordinates are (x%5B1%5D,y%5B1%5D) and (x%5B2%5D,y%5B2%5D), then slope is
+m=%28y%5B1%5D-y%5B2%5D%29%2F%28x%5B1%5D-x%5B2%5D%29

Example: y+=+2x+%2B+1
y+=+2%2A0+%2B+1=>y+=++1 =>b=1 => y-intercept is at (0,1)
y+=+highlight%282%29x+%2B+1=>m=2
to graph it make a table for two points
x|y
0|1...we already have it
-1|-1.....choose any value for x and find the matching value for y; if x=-1 then y+=+2%28-1%29+%2B+1=>y=-1
plot points and draw a line through



Example: you might be given a graph like this
graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-3x+%29%29+
and asked to find the equation of that line y=mx%2Bb
first what we see from the graph is that the line goes through origin; so, we know that b=0
so, your equation will be y=mx%2B0 or just y=mx and we need to find a slope m
as you see from a graph, if x=-1 that y=3 and if x=0 that y=0
so, you have points
(x%5B1%5D,y%5B1%5D)=(0,0)
and
(x%5B2%5D,y%5B2%5D)=(-1,3)


then you can find the slope:
+m=%28y%5B1%5D-y%5B2%5D%29%2F%28x%5B1%5D-x%5B2%5D%29
+m=%280-3%29%2F%280-%28-1%29%29
+m=%280-3%29%2F%280%2B1%29
+m=-3%2F1
+m=-3
and your equation is highlight%28y=-3x%29