Answer: y = 2/3x
Step-by-step explanation: A slope of 2/3 means every time you travel up, two units on a graph, you have to travel over three. this means that if the x-value in our equation was equal to 3, we would have traveled over 3 units, and upwards of two units, which can be calculated with the equation y = 2 / 3 * (3) or (x) equals 2. The way to find the equation mathematically would go as follows.
Use your point (3,2), and add our x-value (3) into the equation.
1. y = (2/3) * 3
[tex]\frac{2}{3}[/tex] * [tex]\frac{3}{1}[/tex] = [tex]\frac{6}{3}[/tex]
2. y = 6/3
6 / 3 = 2
3. y = 2
so our x-value is 3, and our y-value is 2, making the point (3,2)
This proves that the point given falls on the slope without any altered y-intercept. However, when the point falls on a different coordinate, lets say we were given the point (3,3) we would follow the same process.
1. y = (2/3) * 3
[tex]\frac{2}{3}[/tex] * [tex]\frac{3}{1}[/tex] = [tex]\frac{6}{3}[/tex]
2. y = 6/3
6 / 3 = 2
3. y = 2
Well, this doesn't match up with our initial point (3,3), so what went wrong?
There can be a few explanations, the graph could travel up a couple of units from 0 on the y-axis, or down a couple of units. The way to figure this out would be to take the y-value from the point we were given the (3,3) and subtract the y-value we found using our equation, so 2
3 - 2 = 1
What the 1 essentially means is that our graph doesn't start out from zero, somebody places it one unit above our x-axis, so the equation would go as follows.
y = slope(2/3x) + y-intercept(1)
the y-intercept is basically the number of units the graph is moved up or down on the y-axis.
