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-5x+6y=100

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3 Answers

Hi Krissy,
 
      The answer by Vivian L. correctly describes how to find the y-intercept.  Now, let's consider how to find the x-intercept.   
 
The x-intercept is where the graph crosses the X-axis.  At this point, y=0.
So, we plug y=0 into the equation above:
 
-5x + 6(0) = 100
-5x + 0 = 100
x = -20 (dividing both sides by -5).
So, the x-intercept is the point (-20,0).
Vivian got off to a great start, but didn't explain any methods for finding the x-intercept.
 
One way is to manipulate the equation from y = m x + b 
to a new form y = m ( x + b/m) by factoring m out of both terms.
 
For the students who know that
a) the graph of a function f(x-a) is the same as the graph of f(x) except that the graph of f(x-a) will have been translated a units to the right, and 
b) the graph of y = mx (where b is zero) always goes through the origin,
 
this is a great way to apply that knowledge and read-off the x-intercept in a fool-proof way.
 
If you know these two premises are true, you can see that once you have y=mx+b, the x-intercept will be the graph of y = mx shifted m/b to the right, so the x-intercept that was formerly at the origin will now be at m/b.
 
For those who find all of that too confusing, think of it this way:
 
Slope = rise / run
 
Therefore, if we solve that equation for run, we get  Run = rise / slope
 
Therefore, if our y-intercept is b, what run will give us a rise of -b from the y-intercept (which is 0,b)?
 
Plug (-b) into our new formula for "Run":
 
Run = (-b)/m.
 
A run of -b/m means we need to travel horizontally -b/m from the x-position of the y-intercept (0), to reach the x-axis to accumulate a total rise of -b.  Traveling -b/m from 0 puts at the x-coordinate of -b/m.
 
To check this result, use it in the equation.
 
What will be the value of y if x = -b /m ?
 
y = m x + b
y= m (-b/m) + b
But m * (-b/m) is just m(-b/m) (multiplying by m and dividing by m cancels out and has no effect on -b)
y = -b + b
y = 0
 
Therefore, yes, computing -b/m after finding the equation y = mx+b always gives an x-intercept.
 
So go ahead and figure out the x-intercept.
 
 
Hi Krissy;
-5x+6y=100
The standard formula to find x the y-intercept when x=0, is...
y=mx+b
b represents the y-intercept.
So...
-5x+6y=100
We must isolate y...
Let's add 5x to both sides...
5x+-5x+6y=100+5x
6y=5x+100
Let's divide both sides by 6...
6y/6=(5/6)x+100/6
y=(5/6)x+50/3
 
The slope is 5/6
The y-intercept is 50/3
 

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