SOLUTION: I am trying to help my daughter solve the following equation and can't seem to get the right answer, plus it has been 24 years since I have worked algebra. Could you please help m

Algebra ->  Graphs -> SOLUTION: I am trying to help my daughter solve the following equation and can't seem to get the right answer, plus it has been 24 years since I have worked algebra. Could you please help m      Log On


   

Question 88843: I am trying to help my daughter solve the following equation and can't seem to get the right answer, plus it has been 24 years since I have worked algebra. Could you please help me find the solution:
Graph 6x-42=16y

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
6x-42=16y+

%286x-42%29%2F16=cross%2816%2F16%29y+ Divide both sides by 16

6x%2F16-42%2F16=y+ Split up the fraction

%283%2F8%29x-21%2F8=y+ Reduce

y=%283%2F8%29x-21%2F8 Rearrange the sides. So the equation is now in y form

Now lets graph y=%283%2F8%29x-21%2F8

Solved by pluggable solver: Graphing Linear Equations
In order to graph y=%283%2F8%29%2Ax-21%2F8 we only need to plug in two points to draw the line

So lets plug in some points

Plug in x=-9

y=%283%2F8%29%2A%28-9%29-21%2F8

y=-27%2F8-21%2F8 Multiply

y=-48%2F8 Add

y=-6 Reduce

So here's one point (-9,-6)




Now lets find another point

Plug in x=-1

y=%283%2F8%29%2A%28-1%29-21%2F8

y=-3%2F8-21%2F8 Multiply

y=-24%2F8 Add

y=-3 Reduce

So here's another point (-1,-3). Add this to our graph





Now draw a line through these points

So this is the graph of y=%283%2F8%29%2Ax-21%2F8 through the points (-9,-6) and (-1,-3)


So from the graph we can see that the slope is 3%2F8 (which tells us that in order to go from point to point we have to start at one point and go up 3 units and to the right 8 units to get to the next point) the y-intercept is (0,-2.625) ,or (0,-21%2F8), and the x-intercept is (7,0)


We could graph this equation another way. Since b=-21%2F8 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,-21%2F8).


So we have one point (0,-21%2F8)





Now since the slope is 3%2F8, this means that in order to go from point to point we can use the slope to do so. So starting at (0,-21%2F8), we can go up 3 units



and to the right 8 units to get to our next point


Now draw a line through those points to graph y=%283%2F8%29%2Ax-21%2F8


So this is the graph of y=%283%2F8%29%2Ax-21%2F8 through the points (0,-2.625) and (8,0.375)