graph the function in the coordinate plane. use the mark feature tool to indicate the x- and y-intercepts of the function. y=2/3x+4

My blue dot is the y-intercept.

My red dot is my x-intercept.

Please look at the graph.

Step-by-step explanation:

I can show you my graph and mark it where the x-intercepts and y-intercepts are.

Let's begin.

We have y=2/3 x+4.

Compare this to the slope-intercept form, y=mx+b where m is the slope and b is the y-intercept.

You should see that m=2/3 and b=4.

This means the slope is 2/3 and the y-intercept is 4.

Don't forget slope means rise/run.

So once we graph 4 (plot a point) on the y-axis, then we will use our slope to get to one more point.  The slope here tells us to rise 2 and run 3.

Now sometimes our graph is not accurate when drawing by hand so there is a way without graphing that you can find the x- and y-intercepts.

The x-intercept is when the y-coordinate is 0.

The y-intercept is when the x-coordinate is 0.

So to find the x-intercept, I'm going to set y to 0 and solve for x. Like so,

0=2/3 x +4

Subtract 4 on both sides:

-4=2/3 x

Multiply both sides by the reciprocal of 2/3 which is 3/2:

3/2 (-4)=x

Simplify:

-12/2=x

Simplify:

-6=x

Symmetric Property:

x=-6

So the x-intercept is (-6,0).

I actually already have the y-intercept since my equation is in y=mx+b (slope-intercept form).  But if it wasn't you could just set x to 0 and solve for y. Like so:

y=2/3 (0)+4

y=0+4

y=4

The y-intercept is (0,4).

Let's go to our graph now.

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.