SOLUTION: #3 i know how to graph points but how do i solve these type of equations. 3x+4y= 7 # 4 same thing how to i solve to graph these types of equations -x -5y +10 = 0

Algebra ->  Graphs -> SOLUTION: #3 i know how to graph points but how do i solve these type of equations. 3x+4y= 7 # 4 same thing how to i solve to graph these types of equations -x -5y +10 = 0      Log On


   

Question 84056: #3
i know how to graph points but how do i solve these type of equations.
3x+4y= 7

# 4
same thing how to i solve to graph these types of equations
-x -5y +10 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
#3
Solved by pluggable solver: Graphing Linear Equations


3%2Ax%2B4%2Ay=7Start with the given equation



4%2Ay=7-3%2Ax Subtract 3%2Ax from both sides

y=%281%2F4%29%287-3%2Ax%29 Multiply both sides by 1%2F4

y=%281%2F4%29%287%29-%281%2F4%29%283%29x%29 Distribute 1%2F4

y=7%2F4-%283%2F4%29x Multiply

y=%28-3%2F4%29%2Ax%2B7%2F4 Rearrange the terms

y=%28-3%2F4%29%2Ax%2B7%2F4 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=-3%2F4 (the slope) and b=7%2F4 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-7

y=%28-3%2F4%29%2A%28-7%29%2B7%2F4

y=21%2F4%2B7%2F4 Multiply

y=28%2F4 Add

y=7 Reduce

So here's one point (-7,7)





Now lets find another point

Plug in x=-3

y=%28-3%2F4%29%2A%28-3%29%2B7%2F4

y=9%2F4%2B7%2F4 Multiply

y=16%2F4 Add

y=4 Reduce

So here's another point (-3,4). Add this to our graph





Now draw a line through these points

So this is the graph of y=%28-3%2F4%29%2Ax%2B7%2F4 through the points (-7,7) and (-3,4)


So from the graph we can see that the slope is -3%2F4 (which tells us that in order to go from point to point we have to start at one point and go down -3 units and to the right 4 units to get to the next point), the y-intercept is (0,1.75) ,or (0,7%2F4), and the x-intercept is (2.33333333333333,0) ,or (7%2F3,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=7%2F4 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,7%2F4).


So we have one point (0,7%2F4)






Now since the slope is -3%2F4, this means that in order to go from point to point we can use the slope to do so. So starting at (0,7%2F4), we can go down 3 units


and to the right 4 units to get to our next point



Now draw a line through those points to graph y=%28-3%2F4%29%2Ax%2B7%2F4


So this is the graph of y=%28-3%2F4%29%2Ax%2B7%2F4 through the points (0,1.75) and (4,-1.25)



#4
-x-5y%2B10=0
-x-5y=-10 Subtract 10 from both sides
Solved by pluggable solver: Graphing Linear Equations


-1%2Ax-5%2Ay=-10Start with the given equation



-5%2Ay=-10%2B1%2Ax Add 1%2Ax to both sides

y=%28-1%2F5%29%28-10%2B1%2Ax%29 Multiply both sides by -1%2F5

y=%28-1%2F5%29%28-10%29%2B%281%2F5%29%28-1%29x%29 Distribute -1%2F5

y=10%2F5-%281%2F5%29x Multiply

y=%28-1%2F5%29%2Ax%2B10%2F5 Rearrange the terms

y=%28-1%2F5%29%2Ax%2B2 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=-1%2F5 (the slope) and b=2 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-5

y=%28-1%2F5%29%2A%28-5%29%2B2

y=5%2F5%2B2 Multiply

y=15%2F5 Add

y=3 Reduce

So here's one point (-5,3)





Now lets find another point

Plug in x=0

y=%28-1%2F5%29%2A%280%29%2B2

y=0%2F5%2B2 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=%28-1%2F5%29%2Ax%2B2 through the points (-5,3) and (0,2)


So from the graph we can see that the slope is -1%2F5 (which tells us that in order to go from point to point we have to start at one point and go down -1 units and to the right 5 units to get to the next point), the y-intercept is (0,2)and the x-intercept is (10,0) . 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 -1%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 down 1 units


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



Now draw a line through those points to graph y=%28-1%2F5%29%2Ax%2B2


So this is the graph of y=%28-1%2F5%29%2Ax%2B2 through the points (0,2) and (5,1)