Someone please help me

Hey there! I'm happy to help!

Let's think of this as the equation y=mx+b, where m represents the slope and b equals the y-intercept.

The y-intercept is where the line hits the y-axis. As we can see, it hits it at the y-value of zero. Therefore, our equation is just left as y=mx now because b is 0.

We want to find the slope now. This is known as the rise/run, or the y/x. This is basically saying how far up it goes for every one step to the right. If we go to the x-value of one, we see that the y-value is at a little bit less than one. We want to keep on moving to the right until the y-value is at a nice integer value (number without fractions).

If we keep on moving to the right, we see that at the x-value of 3, the y is at 2. This means that the slope is 2/3. And it makes sense! When we were looking at that value of 1, the y-value was less than one and looked like it was at about 2/3, or 0.666

This will apply to all points on the line. Our y will always be 2/3 of what x is.

Therefore, the equation is y=2/3x

I hope that this helps! Have a wonderful day!

468

step-by-step explanation:

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.