SOLUTION: type the correct equation if you are given this coordinates (0,1) (2,-3) (4,-7)

Question 620692: type the correct equation if you are given this coordinates (0,1) (2,-3) (4,-7)
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!
Hi, there--
.
When you are given a series of ordered pairs (x,y) and you want an equation, it sometimes helps to write the x and y values in a table and look for the rate of change (slope).
.
x y
----
0 1
2 -3
4 -7
.
Notice that the x-terms increase by 2 each time, and the y-terms decrease by 4 each time.
.
The rate of change is defined as the "change in y divided by the change in x. Thus the rate of change, or slope, is -4/2=-2.
.
Since the rate of change is constant, we know that we will have the equation for a line. Since we no have the slope and some points on the line, the point-slope form is a good method to use.
.
Next, notice that the point (0,1) is the y-intercept for the equation, the point where the line crosses the y-axis.
.
We can use the slope-intercept form (y=mx+b) to write an equation for the line. THe slope is m and the y-term of the y-intercept is b.
.

.
You can double check your work by making sure that all three points are on this line. Substitute the points for x and y in the equation.
.
(0,1)
y=-2x+1
1=-2(0)+1
1=1
Check!
.
(2,-3)
y=-2x+1
-3=-2(2)+1
-3=-4+1
-3=-3
Check!!
.
(4,-7)
y=-2x+1
-7=-2(4)+1
-7=-8+1
-7=-7
Check!!!
.
Hope this helps! Feel free to email if you still have questions.
.
Ms.Figgy
math.in.the.vortex@gmail.com

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