SOLUTION: 14x + 18y = 10

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Question 114944: 14x + 18y = 10
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Graphing Linear Equations


14%2Ax%2B18%2Ay=10Start with the given equation



18%2Ay=10-14%2Ax Subtract 14%2Ax from both sides

y=%281%2F18%29%2810-14%2Ax%29 Multiply both sides by 1%2F18

y=%281%2F18%29%2810%29-%281%2F18%29%2814%29x%29 Distribute 1%2F18

y=10%2F18-%2814%2F18%29x Multiply

y=%28-14%2F18%29%2Ax%2B10%2F18 Rearrange the terms

y=%28-7%2F9%29%2Ax%2B5%2F9 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=-7%2F9 (the slope) and b=5%2F9 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-7

y=%28-7%2F9%29%2A%28-7%29%2B5%2F9

y=49%2F9%2B5%2F9 Multiply

y=54%2F9 Add

y=6 Reduce

So here's one point (-7,6)





Now lets find another point

Plug in x=2

y=%28-7%2F9%29%2A%282%29%2B5%2F9

y=-14%2F9%2B5%2F9 Multiply

y=-9%2F9 Add

y=-1 Reduce

So here's another point (2,-1). Add this to our graph





Now draw a line through these points

So this is the graph of y=%28-7%2F9%29%2Ax%2B5%2F9 through the points (-7,6) and (2,-1)


So from the graph we can see that the slope is -7%2F9 (which tells us that in order to go from point to point we have to start at one point and go down -7 units and to the right 9 units to get to the next point), the y-intercept is (0,0.555555555555556) ,or (0,5%2F9), and the x-intercept is (0.714285714285714,0) ,or (5%2F7,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=5%2F9 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,5%2F9).


So we have one point (0,5%2F9)






Now since the slope is -7%2F9, this means that in order to go from point to point we can use the slope to do so. So starting at (0,5%2F9), we can go down 7 units


and to the right 9 units to get to our next point



Now draw a line through those points to graph y=%28-7%2F9%29%2Ax%2B5%2F9


So this is the graph of y=%28-7%2F9%29%2Ax%2B5%2F9 through the points (0,0.555555555555556) and (9,-6.44444444444444)