SOLUTION: Review Exercises Chapter 1 Find an equation of the line having the given characteristics. Write the equation using the general form or the slope-intercept form, whichever you p

Question 158031This question is from textbook
: Review Exercises Chapter 1
Find an equation of the line having the given characteristics. Write the equation using the general form or the slope-intercept form, whichever you prefer. Graph each line.
9. Slope = -3; containing the point (2, -1)

y = -3x - 1 this is where I started
This question is from textbook

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First let's find the equation of the line

If you want to find the equation of line with a given a slope of which goes through the point (2,-1), you can simply use the point-slope formula to find the equation:

---Point-Slope Formula---

where is the slope, and

is the given point

So lets use the Point-Slope Formula to find the equation of the line

Plug in , , and (these values are given)

Rewrite as

Distribute

Multiply and to get

Subtract 1 from both sides to isolate y

Combine like terms and to get

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Answer:

So the equation of the line with a slope of which goes through the point (2,-1) is:

which is now in form where the slope is and the y-intercept is

Since 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

Also, because the slope is , this means:

which shows us that the rise is -3 and the run is 1. This means that to go from point to point, we can go down 3 and over 1

So starting at

, go down 3 units

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

Now draw a line through these points to graph

So this is the graph of through the points

and

Also, notice how the graph has a slope of -3 (since ) and it goes through the point (2,-1).
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