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.
