SOLUTION: draw the graph of the following linear function and give the domain and range: h(x)=-2x+3?

Algebra ->  Graphs -> SOLUTION: draw the graph of the following linear function and give the domain and range: h(x)=-2x+3?      Log On


   

Question 181937: draw the graph of the following linear function and give the domain and range: h(x)=-2x+3?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at y=-2x%2B3 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=-2 and the y-intercept is b=3


Since b=3 this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point




Now since the slope is comprised of the "rise" over the "run" this means
slope=rise%2Frun

Also, because the slope is -2, this means:

rise%2Frun=-2%2F1


which shows us that the rise is -2 and the run is 1. This means that to go from point to point, we can go down 2 and over 1



So starting at , go down 2 units


and to the right 1 unit to get to the next point



Now draw a line through these points to graph y=-2x%2B3

So this is the graph of y=-2x%2B3 through the points and


Now notice that the graph extends in both directions along the x-axis. So this means that ANY value of "x" can be plugged into the function.

So the domain is all real numbers.


Also, take note that the graph extends in both directions along the y-axis as well. So this tells us that the range is also ANY number.

So the range is all real numbers.