Finding the equation of a
Line Given Two Points
Mrs. Radigan
How do you write the equation
of a line given two points??
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Given: (3, 6), ( 4, 9)
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How can these points be used to write the
equation of the line they form??
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There are a list of steps on p.214 in your
book and an example for future use.
Mrs. Radigan’s Steps
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Step 1: Find the Slope.
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Step 2: Substitute y, m, and x in y=mx+b.
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Step 3: Solve for b.
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Step 4: Substitute m and b in y=mx+b.
Try out the steps!!
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Given: (3, 6), ( 4, 9)
Step 1: Find the slope.
: (3, 6), ( 4, 9)
x1, y1
x2,
y2
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m = y2 – y1
x2 – x1
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m=9–6=3=3
4-3 1
Step 2: Substitute y, m, and x in
y=mx+b.
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We found m and it was 3.
We have two points each with an x or y to choose.
Given: (3, 6), ( 4, 9)
Choose one point and circle it.
(3, 6), ( 4, 9)
The x I chose is 3 and the y is 6.
Write:
y = mx + b.
Then substitute y, m, and x. 6 = 3(3) + b
Step 3: Solve for b.
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Now solve 6 = 3(3) + b for b.
6 = 3(3) + b
6=9+b
-9 -9
-3=b
Step 4: Substitute m and b in
y=mx+b.
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We found m = 3 and b = - 3.
Write y = mx + b and substitute below.
y = 3x + (- 3)
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Can we write this differently??
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y = 3x – 3 is the same as y = 3x + ( - 3)
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Therefore:
 The
equation of the line through
(3, 6), ( 4, 9) is either
y = 3x – 3 or
y = 3x + ( - 3)
Reviewing the Steps
(These should be committed to memory.)
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Step 1: Find the Slope.
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Step 2: Substitute y, m, and x in y=mx+b.
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Step 3: Solve for b.
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Step 4: Substitute m and b in y=mx+b.