Question 620692
Hi, there--
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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).
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 x  y
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0   1
2 -3
4 -7
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Notice that the x-terms increase by 2 each time, and the y-terms decrease by 4 each time.
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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.
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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.
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Next, notice that the point (0,1) is the y-intercept for the equation, the point where the line crosses the y-axis.
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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.
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{{{y=mx+b}}}
{{{y=-2x+1}}}
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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.
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(0,1)
y=-2x+1
1=-2(0)+1
1=1
Check!
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(2,-3)
y=-2x+1
-3=-2(2)+1
-3=-4+1
-3=-3
Check!!
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(4,-7)
y=-2x+1
-7=-2(4)+1
-7=-8+1
-7=-7
Check!!!
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Hope this helps! Feel free to email if you still have questions.
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Ms.Figgy
math.in.the.vortex@gmail.com