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Equations of Lines
Standard Form
Ax + By = C
x and y on left / constant on right,
no fractions or decimals
Example: 3x + 2y = 4
Slope-Intercept Form
y = mx + b
slope
Algebra 2
Section 9.3 A
Equation of a Line
Example: y = 3x + 4
y-intercept
Point-Slope Form
y – y1 = m(x – x1)
use if given a point and a slope
m = slope.....point is (x1,y1)
Example: y – 2 = 3(x – 5)
Mr. Sims
Get the equation in standard form. {Ax + By = C}
1. 3x = 2y + 5
-2y
2. -y = 4x - 5
- 4x - 4x
-2y
- 4x - y = -5
3x – 2y = 5
no fractions or decimals
in standard form
3. 3x + y + 2 = x – 3 – 9x
3x + y + 2 = -8x – 3 combine like terms
+8x
-2
+8x -2
4. 4 1 x  3 y  8
2
4
2x + 3y = 32
11x + y = -5
Mr. Sims
Get the equation in slope-intercept form. {y = mx + b}
5. x + y = 8
-x
6. 4x + 2y = 18
- 4x
-x
- 4x
2y = - 4x + 18
y = -2x + 9 divide by 2
y = -x + 8
7. -2x + 3y + 5 = 0
-3y
-3y
-3y = -2x + 5
2
5
y x
3
3
divide by - 3
Mr. Sims
A line has the given slope, y-intercept, or contains the points.
Write an equation of the line in standard form. {Ax + By = C}
(x1,y1)
2
8. (2,5), m 
3
y – y1 = m(x – x1) substitute into point-slope form
2
y  (5)  (x  2)
3
2
3 y  5  (x  2)
3
clear out fractions by multiplying
by least common denominator
3y + 15 = 2(x – 2) multiply each term by 3
3y + 15 = 2x – 4 distributive property
-2x -15 -2x -15
-2x + 3y = -19
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(x1,y1)
5
9. (1,6), m 
6
y – y1 = m(x – x1)
substitute into point-slope form
5
y  6  [x  (1)]
6
5
y

6

(x  1) clear out fractions
6
6
6y – 36 = 5(x + 1)
6y – 36 = 5x + 5 distributive property
-5x +36
-5x +36
-5x + 6y = 41
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10. (-2,4) , m = - 4
y – y1 = m(x – x1)
substitute into point-slope form
y – 4 = - 4[x – (-2)]
y – 4 = - 4(x + 2)
y – 4 = - 4x – 8 distributive property
+4x +4
+4x +4
4x + y = - 4
11. m = 3 , b = -2
y = mx + b
substitute into slope-intercept form
y = 3x – 2
-3x -3x
-3x + y = -2
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3
12. m  , b  10
5
y = mx + b
3
5 y  x  10
5
substitute into slope-intercept form
clear out fraction
5y = 3x – 50
-3x -3x
-3x + 5y = -50
13. m = - 4 , b = - 4
y = mx + b substitute into slope-intercept form
y = - 4x – 4
+4x
+4x
4x + y = - 4
Mr. Sims
Algebra 2
Section 9.3 A
Assignment
A line has the given slope, y-intercept, or contains the indicated points.
Write an equation in standard form of each line.
1.) (2,-2) , m = 
4.) m =
1
2
3
, b = -10
5
2.) (-2,-3) , m = -1
3. (3,-2) , m = -3
5.) m = 2 , b = 3
6.) m = -3 , b = 3
7
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