Download y = mx + b

Unit 3 Part 2
Writing Equations
Ax + By = C
(standard form)
y = mx + b
(slope – intercept form)
y = mx + b
is a form of an equation
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What is the equation of a line that has a slope
of ½ and a y-intercept of -3 ?
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y = mx + b
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y=½x–3
Don’t forget the ‘x’
Try these on your own.
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What is the equation of a line that has a slope
of 2 and a y-intercept of -1 ?
y = 2x – 1
What is the equation of a line that has a slope
of ¾ and a y-intercept of 2 ?
y=¾x+2
y = mx + b
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Write the equation of the line whose slope is
2 and contains the point ( 1, 5).
1st substitute into the equation.
y = mx + b
5 = (2)(1) + b
5=2+b
-2 -2
3 = b and ‘m’ = 2
y = 2x + 3
y = mx + b
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Write the equation of the line whose slope is
3 and contains the point ( 2, 8).
1st substitute into the equation.
y = mx + b
8 = (3)(2) + b
8=6+b
-6 -6
2 = b and ‘m’ = 3
y = 3x + 2
y = mx + b
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Write the equation of the line whose slope is
-2 and contains the point ( 4, -9).
1st substitute into the equation.
y = mx + b
-9 = (-2)(4) + b
-9 = -8 + b
+8 +8
-1 = b and ‘m’ = -2
y = -2x – 1
y = mx + b
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Write the equation of the line whose slope is
½ and contains the point ( - 4, -3).
1st substitute into the equation.
y = mx + b
-3 = ( ½ )(- 4) + b
-3 = -2 + b
+2 +2
-1 = b and ‘m’ = ½
y=½x–1
Write the equation of the line
that contains these two points.
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( 1, 3) ( 2, 6)
1st Calculate the slope
Now substitute
y = mx + b
3 = 3(1) + b
3=3+b
-3 -3
0=b
y = 3x + 0  y = 3x
m=
3 – 6 -3
=
1 – 2 -1
=+3
Write the equation of the line
that contains these two points.
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( 3, 4) ( 5, 10)
1st Calculate the slope
Now substitute
y = mx + b
4 = 3(3) + b
4=9+b
-9 -9
-5 = b
y = 3x – 5
m=
4 – 10 -6
=
=+3
3 – 5 -2
Write the equation of the line
that contains these two points.
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( 4, -2) ( -8, 7)
1st Calculate the slope
Now substitute
y = mx + b
-2 = - ¾ (4) + b
-2 = -3 + b
+3 +3
+1 = b
y=-¾x+1
-2 – 7 = -9 = - 3
m=
4
4 – (-8) 12
Write the equation of the line
that contains these two points.
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( -6, -3) ( 0,-5)
1st Calculate the slope
Now substitute
y = mx + b
-3 = - ⅓ (-6) + b
-3 = 2 + b
-2 -2
-5 = b
y=-⅓x–5
-3 –(-5) = 2 = - 1
m=
3
-6 – 0
-6
Write the equation of the line
that contains these two points.
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( -2, -4) ( 2, -2)
1st Calculate the slope
Now substitute
y = mx + b
-4 = ½(-2) + b
-4 = -1 + b
+1 +1
-3 = b
y=½x–3
-4 – (-2) -2
=
m=
-2 – 2 -4
=+½
y – y = m ( x – x)  Formula
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Write the equation of the line that has a slope of
2 and passes through the point ( -6, 4).
1st substitute into the formula.
y – y = m ( x – x)
y – 4 = 2 ( x – (-6))
y–4=2(x+6)
y – 4 = 2x + 12
+4
+4
y = 2x + 16
Can you do it ? Let’s see!
y – y = m ( x – x)  Formula
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Write the equation of the line that has a slope of
-3 and passes through the point ( 1, -2).
1st substitute into the formula.
y – y = m ( x – x)
y – (-2) = -3 ( x – 1)
y + 2 = -3 ( x – 1 )
y + 2 = -3x +3
-2
-2
y = -3x + 1
y – y = m ( x – x)  Formula
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Write the equation of the line that has a slope of
½ and passes through the point ( 4, -3).
1st substitute into the formula.
y – y = m ( x – x)
y – (-3) = ½ ( x – 4)
y+3=½(x–4)
y + 3 = ½x - 2
-3
-3
y=½x-5
y – y = m ( x – x)  Formula
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Write the equation of the line that has a slope of
-¾ and passes through the point ( 8, -1).
1st substitute into the formula.
y – y = m ( x – x)
y – (-1) = -¾ ( x – 8)
y + 1 = -¾ ( x – 8 )
y + 1 = -¾ x + 6
-1
-1
y = -¾ x + 5
y – y = m ( x – x)  Formula
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Write the equation of the line that has a slope of
3 and passes through the point ( -3, 2).
1st substitute into the formula.
y – y = m ( x – x)
y – 2 = 3 ( x – (-3))
y–2=3(x+3)
y – 2 = 3x + 9
+2
+2
y = 3x + 11