Download Algebra I Chapter 5 Section 3

CC Math I Standards: Unit 5
SLOPE-INTERCEPT FORM: Part 1
Warm Up Activity:
1) Find slope of (3, 12) and (6, -6) 2) Find slope of (4, 8) and (-5, 8)
3) Find slope of (-5, 2) and (7, 6)
What is the Y – INTERCEPT of a line?
The POINT where the line crosses the y – axis is called the y-intercept = (0, b)
y
Identify the y-intercept of each line
 Y-AXIS: vertical axis
 Follow the line until it reaches y- axis
o Draw Intercept point
o Find the coordinate of that point
Example: Line #1: Line #1 cross the y-axis at (0 , 5)
Line #2:
Line #7
Line #1
Line #2
Line #3:
x
Line #4:
Line #5:
Line #6:
Line #7:
Line #4
Line #3
Line #5
What is Slope-Intercept Form?
Line #6
Identify the Slope and Y-Intercept in each of the following equations:
1) y = 3x + 5
5) y = 112 + 87x
2) y = 7 + 9x
6) 0.4x – 2 = y
3) -4x – 3 = y
7) y 
9) y 
2
1
x
3
3
10) y 
x 5

2 6
1
x
4
11) 6 – 7x = y
4) 2 
6
x y
7
8)
7
 5x  y
9
12) y = 23
Write the Equation of a line given slope and y – intercept:
1) b = 17/5 and m = 3
2) Slope of 3 and y – intercept is 5.
3) m = ¼ and (0, -6)
4) Slope of -2 and (0, 4)
5) b = 5/7 and m = -3/7
6) Y – intercept is -2 and slope is - ¼.
Write the Equation of a line in each graph:


IDENTIFY the y-intercept (b) of the line and the slope (m) of the line
WRITE y = mx + b equation by substituting m and b values.
1) Slope:
2) Slope:
3) Slope:
Y – Intercept:
Y – Intercept:
Y – Intercept:
Equation:
Equation:
Equation:
4) Slope:
5) Slope:
6) Slope:
Y – Intercept:
Equation:
Y – Intercept:
Equation:
Y – Intercept:
Equation:
GRAPHING LINES BY HAND: How do you graph a line in slope intercept form?
1) PLOT the y – intercept.
2) From y – intercept perform SLOPE (RISE over RUN) to plot a second point.
3) Draw a line between the two points.
2
3
1) y   x  1
y  x3
5)
3
2
y-intercept =
y-intercept =
Slope =
Slope =
Rise =
Rise =
Run =
Run =
2)
1
x2  y
2
6) y  
5
x4
4
y-intercept =
y-intercept =
Slope =
Slope =
Rise =
Rise =
Run =
Run =
3) y = 1 – 4x
7) y  2 x
y-intercept =
y-intercept =
Slope =
Slope =
Rise =
Rise =
Run =
Run =
4) y = 3x - 2
8) y  3 
1
x
3
CC Math I Standards: Unit 5
SLOPE-INTERCEPT FORM: Part 2
1) Identify the SLOPE and Y-INTERCEPT in each equation:
1a. y 
5
x6
7
1b. y 
1
 3x
2
LINE #1
LINE #2
1
3
1c. y  x 
6
2
1e. y  8 
1d.  9 x  8  y
2
x
9
1f.
5 4
 x  y
8 7
LINE #3
2)Write the SLOPE-INTERCEPT FORM for each line:
Line #1 Equation:
Line #2 Equation:


Line #3 Equation:
HOW DO YOU DETERMINE IF A POINT IS ON A LINE?
For each point (x, y), SUBSTITUTE the x-value and y-value into the equation.
CHECK if both sides of the equation
o If EQUAL SIDES, then point IS on line
o If NOT EQUAL SIDES, the point IS NOT on line
Example: y = 3x – 4
Check: (1, -1)
(2, 6)
PRACTICE PROBLEMS:
1) y  2 x  15
Check: (1, 12) , (-3, 21), (2, 11)
2) y  1  4 x
3) y  5 
1
x
2
(-3, 13)
4) y  
3
x7
4
Check: (-2, -7), (3, 44), 6, 25)
5) y  3 x  8
Check: (8, 1), (4, 3), (-6, 2)
6) y 
2
x 1
3
(-4, -16)
(5, 11)
Check: (12, -16), (-4, 4), (4, 4)
Check: (3, -1) , (1, -5), (0, 8)
Check: (6, 3), (-3, -1), (-9, -5)
REVIEW: Graph a line for each of the following for a given point and a slope.
1) point = (0, -2); m = 5/2
2) point = (2, 1) ; m = -3/2
3) point = (-3,4); m = -1
Based on graphs above, write equation of each line in SLOPE-INTERCEPT FORM:
1)
2)
3)
How do we find the equation of a line without graphing?
CASE #1: FIND THE Y-INTERCEPT of a line when you have the slope and any point.
What is the equation for slope-intercept form?
Example #1: Line that passes through (1, 5) and has a slope of 2.
Step #1: SUBSTITUTE known values into slope- intercept form
Step #2: SOLVE for b.
Step #3: WRITE the equation with x and y as variables
Example #2: Line that passes through (2, -3) with slope of ½.
Step #1 and 2:
Step #3: Equation
Find Equation in Slope-Intercept Form…
Example 3: Line that passes through (1, -4) with a slope of –5/2.
Step #1 and 2:
Step #3: Equation
Example 4: Line that passes through (5, 5) with a slope of 1/3.
Example 5: Line that passes through (-9, 8) with a slope of -5/3.
Example 6: Line that passes through (-3, -7) and m = 4.
SPECIAL CASE: UNDEFINED SLOPE
1) Write an equation of a line that passes through (1, 3) with a slope of UNDEFINED.
2) Write an equation of a line with an undefined slope through the point (-2, 12).
3) Write an equation of a line has y-intercept of 5 with an undefined slope.
CLASSROOM WORK: Use a separate piece of paper,
Write an equation of a line that passes through each point with the given slope.
1) (-3, 3) and m = 1;
3) (1, 6) and m = ½;
5) (5, -3) and slope = 3/2;
2) (0, 6) and slope = -2;
4)
m = -3/5 and (4, -3);
6) (4, -2) and m = 0;
CC Math I Standards: Unit 5
Review of Last Week
1) State the SLOPE Formula:
2) Find the slope of the line for each pair of points:
2a. (3, 4) and (5, 8)
2c. (6, -4) and (8, -4)
2b. (-2, -9) and (-3, -6)
2d. (2, 3) and (-5, -1)
2e. (7, 2) and (7, -2)
2f. (-5, 7) and (1, -2)
3) State the SLOPE INTERCEPT FORM Equation for a line:
4) For each graph, FIND the slope and y-intercept to write the equation of the line:
5) For the given point (x, y) and slope, m, find the SLOPE INTERCEPT FORM of line.
STEP by STEP Example: (4, 2) and slope = 3
What do you know?
y=2
Substitute and Solve
y = mx + b
x=4
2 = 3*4 + b
m=3
2 = 12 + b
y = 3x – 10
b = ??
-10 = b
Keep x and y as variables.
5a. (0, 1) and slope = 1/3
5d. (10, -3) and m = 0
5b. m = -2 and (-1, 3)
5e. (9, 11) and m 
5c. (-5, -3) and m 
3
5
2
3
Write Equation
y = mx + b
5g. (14, 6) and m 
3
7
5h. (2, -4) and m = -1
5f. slope = 4 and (0, -7)
5i.
5
m   and (6, 7)
2
CC Math I Standards: Unit 5
SLOPE-INTERCEPT FORM: Part 3
Find the SLOPE-INTERCEPT FORM of a line when given ANY two points on the line?
3 STEP PROCESS: Given two points (x1, y1) and (x2, y2) on a line
y2  y1
m

Step 1: FIND the SLOPE of line:
(REDUCE FRACTIONS!!!!)
x2  x1
Step 2: PICK one point and the slope to FIND the Y-INTERCEPT.
o (x1,y1) and m
o Find the y-intercept (b) for y1 = m x1 + b
(REDUCE FRACTIONS!!!!)
Step 3: WRITE the equation of the line in SLOPE-INTERCEPT FORM.
o Use the m from Step 1 and b from Step 2
o y = mx + b
STEP BY STEP: Find the Slope Intercept Form of the line through (5, 7) and (3, 1).
#1: SLOPE
(5, 7) and (3, 1).
m
y2  y1 1  7

x2  x1 3  5
m3
#2: Y-INTERCEPT
m  3 and (5, 7)
#3: EQUATION
y = mx + b
y = mx + b
7  35  b
y = 3x – 8
-8 = b
Keep x and y as variables.
Example 1: Find the Slope Intercept Form of the line through (-3, 2) and (5, -14)
Example 2: Find the equation of the line that passes through (4, 7) and (8, 12).
Example 3: Find the equation of the line that passes through (0, 6) and (5, 0).
Example 4: Find the Slope Intercept Form of the line through (3, 4) and (-2, 4).
Example 5: Find the Slope Intercept Form of the line through (-1, 3) and (4, -1).
SPECIAL CASE: Find the equation of the line that passes through (-1, 3) and (-1, -8).
CLASSWORK PRACTICE: Use Separate paper as needed.
Find the Slope Intercept Form of the line through each of points.
1. (3, -5) and (6, 4)
4. (2, -4) and (2, 6)
7. (6, 2) and (4, 4)
2. (-2, 20) and (2, 4)
5. (-4, -5) and (6, -1)
8. (4, 5) and (-3, -1)
3. (0, -3) and (2, 0)
6. (3, -3) and (1, -3)
9. (-2, -7) and (8, 8)
CC Math I Standards: Unit 5
SLOPE-INTERCEPT FORM: Part 4
Find Slope Intercept Form of a Line when given a Linear Equation
Y Coefficient of One Case
SIMPLIFY and MOVE “x terms” or “number terms” by addition or subtraction
For Problems #1 – 6: SOLVE for y, then IDENTIFY the Slope and Y-Intercept
1) 3x = 5 + y
2) y – 8 = 2x + 3
4) 7 = 6x + y – 2
5) 5(7 – x) = y
3)
y
5
x3
3
6) y – 3x + 5 = 12
For Problems #7 – 12: Find Slope Intercept Form AND GRAPH the Line
 Identify the Slope and Y-Intercept
7) 1 = -3x + y
8) y + 7 = x + 3
9) 2(x – 2) = y
10) y  4 
2
x3
3
11) -2x + y = 0
12) y 
4
x3
3
CC Math I Standards: Unit 5
SLOPE-INTERCEPT FORM: Part 5
Find Slope Intercept Form of a Line when given a Linear Equation




Non-One Coefficients of y Case
Simplify both sides (if needed)
Move “x terms” or constants by addition or subtraction to one side
Divide all terms by the coefficient of y
REDUCE All Fractions
Example 1: 3y + 6x = 10
Example 2: 10y – 5x = 8
Example 3: 8x – 4y = 12
Practice Problems: Solve for Slope Intercept Form and Identify the slope and y-intercept
1) 9y – 3x = 18
4) x – 5y = 6
7) 15 = -7x + 6y
2)
8x - 2y = 7
5)
x + 5y = 8
8)
9 = 4y – x
3)
14y – 35x = 63
6)
21 = 7y – 2x
9)
9x + 3y = 0