Find the x-intercept and the y-intercept from the
following linear equation:
4x + 8y = 64
x-intercept ([?], [ ]
y-intercept ([ ], [ ])

9514 1404 393

  x-intercept: (16, 0)

  y-intercept: (0, 8)

Step-by-step explanation:

Each intercept is found by setting the other variable to zero and solving for the variable of interest.

I like to find the intercepts from this form because it basically involves dividing the constant by the variable coefficient.

x-intercept

  y = 0, so we have 4x = 64   ⇒   x = 64/4 = 16

  x-intercept is (16, 0)

y-intercept

  x = 0, so we have 8y = 64   ⇒   y = 64/8 = 8

  y-intercept is (0, 8)

Additional comment

There is a form of the linear equation called the "intercept form" that looks like this:

  x/a +y/b = 1

where 'a' is the x-intercept and 'b' is the y-intercept.

You can get this form by dividing the standard form equation by the constant. Here, that gives ...

  4x/64 +8y/64 = 1

  x/16 +y/8 = 1

This is nice because it gives both intercepts with one operation (divide by the constant). It's easy enough to do, but not always easy to explain. This form of the equation of a line is rarely seen.

the answer i think is 1 exit.