Verify that (0,4) is on the line 3x+2y=8. Find another point on this line.

Question

use the points to find the slope of the line.

Answer 1

If the point is on the line, then it satisfies the equation, that is, it balances the equation and makes it a true statement.

We can check this by plugging in the numbers. 

In the ordered pair given, x =0 and y = 4. 

So the equation would look like this:

3(0) + 2(4) = 8 

  0    +   8   = 8

yes, the equation balances! 

 

We can find another point on the line several ways. One is to start by rearranging the equation into y intercept form (y = mx + b). Move the 3x to the right side by subtracting it and they divide everything by 2:

 

y = -3x + 8

           2

 

now we can see, that the slope is -3/2 and that the y intercept is 8/2 or +4, (which we already knew).

 

so start at our other point (0,4) and move down 3 units (equivalent to a negative "rise") and right 2 units (a positive "run")  You end up at (2,1)