You have the following equation of a line:
y = -2/3 x + 4
In order to sketch the graph of the given equation you can calculate the value of y for some values of x inside a definite interval. If you choose the interval (-3,3) for x, then the values of y in this interval will be:
y(-3) = (-2/3)(-3) + 4 = 6
y(-2) = (-2/3)(-2) + 4 = 16/3
y(-1) = (-2/3)(-1) + 4 = 13/3
y(0) = (-2/3)(0) + 4 = 4
y(1) = (-2/3)(1) + 4 = 10/3
y(2) = (-2/3)(2) + 4 = 8/3
y(3) = (-2/3)(3) + 4 = 2
summarizing, you have:
x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
y | 6 | 16/3 | 13/3 | 4 | 10/3 | 8/3 | 2 |
The following image is a graph of the function