Provide three points on a graph for the equation y = -2/3x + 4.
I have the points (0, 4) and (6, 0).
Do you have any idea what a 3rd one might be?
Ther are an infinite number of possibilities. Just pick any x you like (except for the two you already have) and compute the y for that point, using the equation.
For example, if x = 3, y = -2 + 4 = 2
You could also pick any y and compute the x, using x = (3/2)(4-y), which is the same function, rearranged.
To find a third point on the graph of the equation y = -2/3x + 4, you can either choose another x value and calculate the corresponding y value or choose another y value and calculate the corresponding x value.
Let's start by choosing another x value. Since you already have the points (0, 4) and (6, 0), let's choose x = 3. Now we can substitute this x value into the equation to calculate the y value:
y = -2/3(3) + 4
y = -2 + 4
y = 2
Therefore, when x = 3, y = 2. So the third point on the graph is (3, 2).
Alternatively, you can choose another y value and calculate the corresponding x value by rearranging the equation.
Using x = (3/2)(4-y), let's choose y = 1:
x = (3/2)(4-1)
x = (3/2)(3)
x = 9/2
x = 4.5
So when y = 1, x = 4.5. Thus, the third point on the graph is (4.5, 1).
Remember, there are infinite possible points that can be plotted on the graph, so you can choose any values for x or y (except for the ones you already used) and calculate the corresponding value using the equation to find more points.