SOLUTION: I need help, i'm not all that great at the kind of algebra i'm doing. I need three coordinates for the following problem: 2x + -5y = 10.

Algebra ->  Linear-equations -> SOLUTION: I need help, i'm not all that great at the kind of algebra i'm doing. I need three coordinates for the following problem: 2x + -5y = 10.      Log On


   

Question 83032: I need help, i'm not all that great at the kind of algebra i'm doing. I need three coordinates for the following problem: 2x + -5y = 10.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to find 3 points, lets graph the equation 2x+%2B+-5y+=+10
Solved by pluggable solver: Graphing Linear Equations


2%2Ax-5%2Ay=10Start with the given equation



-5%2Ay=10-2%2Ax Subtract 2%2Ax from both sides

y=%28-1%2F5%29%2810-2%2Ax%29 Multiply both sides by -1%2F5

y=%28-1%2F5%29%2810%29%2B%281%2F5%29%282%29x%29 Distribute -1%2F5

y=-10%2F5%2B%282%2F5%29x Multiply

y=%282%2F5%29%2Ax-10%2F5 Rearrange the terms

y=%282%2F5%29%2Ax-2 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=2%2F5 (the slope) and b=-2 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-5

y=%282%2F5%29%2A%28-5%29-2

y=-10%2F5-2 Multiply

y=-20%2F5 Add

y=-4 Reduce

So here's one point (-5,-4)





Now lets find another point

Plug in x=0

y=%282%2F5%29%2A%280%29-2

y=0%2F5-2 Multiply

y=-10%2F5 Add

y=-2 Reduce

So here's another point (0,-2). Add this to our graph





Now draw a line through these points

So this is the graph of y=%282%2F5%29%2Ax-2 through the points (-5,-4) and (0,-2)


So from the graph we can see that the slope is 2%2F5 (which tells us that in order to go from point to point we have to start at one point and go up 2 units and to the right 5 units to get to the next point) the y-intercept is (0,-2)and the x-intercept is (5,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=-2 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,-2).


So we have one point (0,-2)






Now since the slope is 2%2F5, this means that in order to go from point to point we can use the slope to do so. So starting at (0,-2), we can go up 2 units


and to the right 5 units to get to our next point



Now draw a line through those points to graph y=%282%2F5%29%2Ax-2


So this is the graph of y=%282%2F5%29%2Ax-2 through the points (0,-2) and (5,0)



Since we found 2 points through graphing, we can find one more by looking at the slope. Since the slope is 2%2F5 that means we start at a given point and go up 2 units and go to the right 5 units to get our next point. So lets start at (5,0): lets go up two units and over 5 units to get (10,2). So we've now found 3 points which are:
(0,-2),(5,0), and (10,2)