How do you find a standard form equation for the line #f(-4) = 0# , #f(0) = 2#?

1 Answer
Noah G
Apr 15, 2017

The equation is #x - 2y + 4 = 0#

Explanation:

Consider the basics of function notation: #f(x) = y#. This means that the line is guaranteed to pass through the points #(-4, 0)# and #(0, 2)#. Now, by the slope formula, we have:

#m = (y_2 - y_1)/(x_2 - x_1)#

#m = (2 - 0)/(0 - (-4))#

#m = 2/4#

#m = 1/2#

Now we find the equation using point-slope form.

#y- y_1 = m(x - x_1)#

#y - 0 = 1/2(x - (-4))#

#y = 1/2x + 2#

Convert to standard form, which is represented by #Ax +By - C= 0#.

#0 = 1/2x - y + 2#

Since the coefficients must be integers, we must multiply both sides by #2#.

#0 = x - 2y + 4#

Hopefully this helps!

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