Question

Draw the graphs of the equations y=8/3x and y=-8/3x on the same coordinate plane. Name their point of intersection as p. State the coordinate of the point p.​

Answer 1

Here we want to graph the equations:

f(x) = y =(8/3)*x

and

g(x) = y = -(8/3)*x

To graph these you need to find some coordinate points of each one, and then connect them, such that the graph of these two equations can be seen below.

Where the blue one is f(x) and the green one is g(x)

We now want to look at the graph and find the point of intersection p.

By looking at the graph below, we can see that the intersection is at the origin, then p = (0,0)

Also remember that an intersection of two functions means that:

f(x) = g(x)

for that particular x value, then we can solve this for our functions and get:

(8/3)*x = -(8/3)*x

That equation is only true when x = 0

Then we have the intersection at x = 0, and the correspondent y value is given by f(0) or g(0) (will be the same value)

y = f(0) = (8/3)*0 = 0 = -(8/3)*0 = g(0)

Then we also found analytically that the intersection is in the point (0, 0)