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SWBAT… Write and graph lines in slope-intercept form Mon, 11/14
Agenda1. WU (10 min)2. Video on graphing (5 min)3. Graphing lines (10 min)4. Writing equations of lines in slope-intercept form
Warm-Up: Solve each equation for y:1. 2y = 4x + 22. -3y = -9x – 123. 21x – 7y =144. 2y + 26 = -6x
HW5: Writing and graphing equations in slope-intercept form
When an equation is in slope-intercept When an equation is in slope-intercept form:form:
When an equation is in slope-intercept When an equation is in slope-intercept form:form:
What is the slope? ____________
2 1y x Now look at the equation below……
What is the y-intercept? ____________
Converting linear Converting linear equations into Slope-equations into Slope-
Intercept FormIntercept Form
Converting linear Converting linear equations into Slope-equations into Slope-
Intercept FormIntercept Form
4 Warm-UP Examples4 Warm-UP Examples4 Warm-UP Examples4 Warm-UP Examples
Slope intercept form is:
y = mx + b
Our main goal is to get the y alone on one side of the equation
Example 1 - convert into Slope-Intercept Form
Example 1 - convert into Slope-Intercept Form
2 4 2y x 2 2
2 4 2y x 2 2 2
(divide both sides by 2 to get y alone)
2 4 2y x
(now simplify all fractions)2 1
2 1y x What is the slope? _____ What is the y-intercept? ______
Example 2 – Convert to Slope-Intercept Form
-3y = -9x – 12Step 1: divide both sides by -3 to get y alone
Step 2: Simplify all fractions
Step 3: Write your equation in y = mx + b
What is the slope? ____________
What is the y-intercept? ____________
*** Check Your Answer ***
-3y = -9x – 12 (divide both sides by -3 to get y alone)
(now simplify all fractions)
y = 3x + 4
-3 -3
-3y = -9x – 12-3 -3 -3
Slope = 3
Intercept = 4
Wow, you’re good at this!!
Example 3: Convert to Slope-Intercept Form
21x – 7y =14 (subtract both sides by 21x)
-7y = -21x + 14(now divide both sides by -7)
y = 3x – 2
(simplify all fractions)
21 -21xx
7 - 7 -7
What is the slope? _________
What is the y-intercept? ________
2y + 26 = -6x
Step 1: Subtract both sides by 26
Step 2: Divide both sides by 2 to get y by itself
Step 3: Simplify all fractions
Example 4: Convert to Slope-Intercept Form
What is the slope? ____________
What is the y-intercept? ____________
2y + 26 = -6x(subtract both sides by 26)
2y = -6x – 26(now divide both sides by 2
y = -3x – 13
(simplify all fractions)
You are a math wizard!
*** Check Your Answer ***
26 -26
2 2 2
Families of Linear Graphs
• http://www.glencoe.com/sites/texas/student/mathematics/assets/animation/algebra1/ALG1CIM4-3.swf
1 2 3 4 5
1
2
3
4
5
-1
-2
-3
-4
-5
-1-2-3-4-5 0
Step 2: Look at the Step 2: Look at the y-intercepty-intercept and and plot plot where the graph crosses the y-axis.where the graph crosses the y-axis.
Step 3: Use the Step 3: Use the slopeslope (rise/run) to determine (rise/run) to determine the next point and the next point and plot.plot. Slope = 2/3 = Slope = 2/3 = 22//33Step 4: Draw a line Step 4: Draw a line through both points. through both points. Be sure to extend the Be sure to extend the line and put arrows at line and put arrows at both ends. (Use a both ends. (Use a ruler!)ruler!)
y = 2/3x + 2 y
x
Step 5: Label your lineStep 5: Label your line
Step 1: Solve for yStep 1: Solve for y y = 2/3x + 2
1 2 3 4 5
1
2
3
4
5
-1
-2
-3
-4
-5
-1-2-3-4-5 0
Step 2: Look at the Step 2: Look at the y-intercepty-intercept and and plot plot where the graph crosses the y-axis.where the graph crosses the y-axis.
Step 3: Use the Step 3: Use the slopeslope (rise/run) to determine (rise/run) to determine the next point and the next point and plot.plot. Slope = 2 = Slope = 2 = 22//11Step 4: Draw a line Step 4: Draw a line through both points. through both points. Be sure to extend the Be sure to extend the line and put arrows at line and put arrows at both ends. (Use a both ends. (Use a ruler!)ruler!)
y = 2x + 1
x
y
Step 5: Label your lineStep 5: Label your line
Step 1: Solve for yStep 1: Solve for y
1 2 3 4 5
1
2
3
4
5
-1
-2
-3
-4
-5
-1-2-3-4-5 0
Step 2: Look at the Step 2: Look at the y-intercepty-intercept and and plot plot where the graph crosses the y-axis.where the graph crosses the y-axis.
Step 3: Use the Step 3: Use the slopeslope (rise/run) to determine (rise/run) to determine the next point and the next point and plot.plot. Slope = -1 = -Slope = -1 = -11//11Step 4: Draw a line Step 4: Draw a line through both points. through both points. Be sure to extend the Be sure to extend the line and put arrows at line and put arrows at both ends. (Use a both ends. (Use a ruler!)ruler!)
y = -x – 2
y
x
Step 5: Label your lineStep 5: Label your line
Step 1: Solve for yStep 1: Solve for y
Write the equation of the line, in slope-intercept form, that passes through (3, 5) and (5, 9)
m = (y2-y1)/(x2-x1)Step 1: Find the slopem = (9-5)/(5-3) = 4/2 = 2
Step 2: Plug in either coordinate into y = mx + b and solve for b
Step 3: Write the equation of the line by substituting the values you computed for m (step 1) and b (step 2) in y = mx + b
y = 2x – 1
(3, 5) (5, 9)y = mx + b y = mx+b
5 = 2(3) + b OR 9 = 2(5) + b5 = 6 + b 9 = 10 + b-1 = b -1 = b
Besides (3, 5) and (5, 9), what’s another point on this line? Hint: b=-1(0, -1)
Ex1:Write the equation of the line, in slope-intercept form, that passes through (3, 5) and (5, 9)
m = (y2-y1)/(x2-x1)Step 1: Find the slopem = (9-5)/(5-3) = 4/2 = 2
Step 2: Plug in either coordinate into y = mx + b and solve for b
Step 3: Write the equation of the line by substituting the values you computed for m (step 1) and b (step 2) in y = mx + b
y = 2x – 1
(3, 5) (5, 9)y = mx + b y = mx+b
5 = 2(3) + b OR 9 = 2(5) + b5 = 6 + b 9 = 10 + b-1 = b -1 = b
SWBAT… Write equations in slope-intercept form Tues, 1/4
Agenda1. WU (15 min)2. Review hw#5 (15 min)3. Quiz (15 min)
WARM-UP: Write the slope-intercept form of an
equation of the line that satisfies each condition:
1.) Has slope 3 and y-intercept -52.) Passes through (5, -7) and has a slope of 33.) Passes through (6, -3) and (12, -3)4.) Has an x-intercept of -2 and a y-intercept of
4 (Hint: write the two points)
2 problems