make a table of values for thsi equation with at least 4 points in each table.
2x-3y=4
then I isolated y to y=2/3x-4/3
how do I find points where both x and y are whole numbers? How do I find the "nice" points so it is easier to graph?
Trial and error really for x and y being whole numbers. You have to see, for example, how many 2's [the 2x bit] to take away from 4 [on the RHS] before it's divisible by -3 [from the 3y bit]
For example, from -3y = 4 - 2x
x = 5 will give -3y = 6 which means y = -2
The best points are usually where it cuts the axes.
Set y=0 to find where it cuts the x axis
Set x=0 to find where it cuts the y axis
you will get the points
(2, 0) and (0, -4/3) respectively.
Hope that helps
y=2/3x-4/3 or
y = (2x-4)/3
you want the numerator to be a multiple of 3
by "trial and error", if x = 5
y = (10-4)/3
= 2
so one "nice" is (5,2)
once you have one point to find more just add multiples of 3 to your choice of x
e.g x = 5+12 or 17 should work
check: y = (34-4)/3 = 10
To find points where both x and y are whole numbers, you can choose different values for x and calculate the corresponding values for y using the equation y = (2/3)x - 4/3.
To make it easier to graph, it's helpful to choose "nice" points, which are usually integers or values that simplify the calculations. Here's how you can find nice points:
1. Choose different values for x that are whole numbers. Let's start with 0, 3, 6, and 9.
For x = 0:
- Substitute x = 0 into the equation: y = (2/3)(0) - 4/3 = -4/3
- So, one point is (0, -4/3).
For x = 3:
- Substitute x = 3 into the equation: y = (2/3)(3) - 4/3 = 2 - 4/3 = 2/3
- So, another point is (3, 2/3).
For x = 6:
- Substitute x = 6 into the equation: y = (2/3)(6) - 4/3 = 4 - 4/3 = 8/3
- Another point is (6, 8/3).
For x = 9:
- Substitute x = 9 into the equation: y = (2/3)(9) - 4/3 = 6 - 4/3 = 14/3
- Another point is (9, 14/3).
2. Repeat the process for other whole number values of x to find additional points.
By following this method, you can find "nice" points where both x and y are whole numbers. Remember to simplify any fractions obtained from the calculations.