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find coordinates for x and y intercept

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Noel D. | Stanford Ph. D. available for chemistry and math tutoring.Stanford Ph. D. available for chemistry ...
4.9 4.9 (604 lesson ratings) (604)
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).
Isaak B. | Good (H.S. or College Math, Physics, Chem, EE Engineering) Cheap TutorGood (H.S. or College Math, Physics, Che...
4.9 4.9 (845 lesson ratings) (845)
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.
Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
Hi Krissy;
The standard formula to find x the y-intercept when x=0, is...
b represents the y-intercept.
We must isolate y...
Let's add 5x to both sides...
Let's divide both sides by 6...
The slope is 5/6
The y-intercept is 50/3