do now 1. solve the equation 2. find the x-intercept and the y-intercept of the equation +4x 2 + 5x...
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Do Now
1. Solve the equation
2. Find the x-intercept and the y-intercept of the equation
€
2(1 − x) + 3x = −4(x + 2)
€
5x + y = 25
€
2 − 2x + 3x = −4 x − 8
2 + x = −4 x − 8+4x +4x
2 + 5x = -8-2 -2
5x = -10
5 5
x = -2
5x + (0) = 25
5x = 25
x = 5
(5,0)
5(0) + y = 25
y = 25 (0,25)
S
Important!!!This is one of the big concepts in
Algebra 1. You need to thoroughly understand this!Slope – Intercept Form
y = mx + bm represents the slope
b represents the y-intercept
To find the slope and y-intercept of an equation, write the equation in slope-intercept form: y = mx + b.
Find the slope and y-intercept.
1) y = 3x – 7
y = mx + b
m = 3, b = (0,-7)
Find the slope and y-intercept.
2) y = x
y = mx + b
y = x + 0
3) y = 5
y = mx + b
y = 0x + 5
2
3 m =
b = (0,0)
2
32
3
m = 0b = (0,5)
HORIZONTAL LINE
-3 -3 -3
Find the slope and y-intercept.4) 5x - 3y = 6
Write it in slope-intercept form. (y = mx + b)
5x – 3y = 6
-3y = -5x + 6
y = x - 25
3
m =
b = (0,-2)
5
3
Write it in slope-intercept form. (y = mx + b)
2y + 2 = 4x
2y = 4x - 2
y = 2x - 1
Find the slope and y-intercept. 5) 2y + 2 = 4x
2 2 2 m = 2b = (0,-1)
Find the slope and y-intercept of y = -2x + 4
1. m = 2; b = 4
2. m = 4; b = 2
3. m = -2; b = 4
4. m = 4; b = -2
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
When an equation is in slope-intercept form:
What is the slope? ____________
2 1y x Now look at the equation below……
What is the intercept? ____________
1 2 3 4 5
1
2
3
4
5
-1
-2
-3
-4
-5
-1-2-3-4-5 0
Step 1: Look at the y-intercept and plot where the graphs cross the “y” axis.
Now look at the graph of the line.
Step 2: Use the slope (rise/run) to determine the next point and plot.
Step 3: Draw a line through both points. Be sure to extend pass point and put arrow at both ends.
*** Easy ***
5y = 10x + 15Convert to Slope-Intercept Form:
(divide both sides by 5 to get y alone)
(now simplify all fractions)
y = 2x + 3 BRAVO!!
5 10 15y x 5 5
5 10 15y x 5 5 5
*** Now Try this Convert to
Slope-Intercept Form ***
-3y = -9x - 12
Step 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 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!!
*** medium ***
21x – 7y =14Convert to Slope-Intercept Form:
(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
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
*** Now Try this Convert to Slope-
Intercept Form ***
What is the slope? ____________
What is the 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
Slope-Intercept Fromy = mx + b
What are the two things we see/use in this form?
1. m = Slope
2. b = y-intercept
Could you make an equation if I gave you:
m = 2
b = (0,6)
€
y = 2x + 6
Ex 1 Write the slope-intercept form using
Slope-intercept form
Replace m with and b with –4.
Answer: The equation is
Write an Equation Given Slope and y-intercept
Ex 2 Write the slope-intercept form using
Answer: The equation is
Slope-intercept form
Replace m with –4 and b with –16.
Write an Equation Given slope and y-int.
Create an equation using the given information:
1. Slope = 3y-intercept = (0,-6)
2. Slope = -2y-intercept = (0,7)
3. Slope = 2/5y-intercept = (0,-10)
€
y = 3x − 6
€
y = −2x + 7
€
y =2
5x −10
Write the equation of a line that has a y-intercept of -3
and a slope of -4.
1. y = -3x – 4
2. y = -4x – 3
3. y = -3x + 4
4. y = -4x + 3
Write the Equation of a Line from a Graph
Where does the line cross the y-axis?◦ At the point (0, -4)◦ The y-intercept is -4.
What is the slope of the line?◦ The graph also crosses
the x-axis at (2, 0).◦ We can use the slope
formula to find our slope.
m = -4 – 0 = -4 = 2 0 – 2 -2
We know our slope is 2 and our y-intercept is -4, what is the equation of our line?
y = mx + by = 2x + (-4)y = 2x -4
Let’s try some examples! Write the equation of a
line with a slope of -2 and a y-intercept of 6.
y = mx + b y = -2x + 6
Write the equation of a line with a slope of -4/3 and a y-intercept of 1.
y = mx + b y = (-4/3) + 1
Using a graph Where does the line
cross the y-axis?◦ At the point (0, 2)◦ So the y-intercept b is 2.
The line also passes through the point (3, 0).
We can use these points to find the slope of the line. How? What formula do we use?◦ Using the slope formula,
we find that the slope m is -2/3.
◦ Write the equation of the line.
y= mx + b y = (-2/3)x + 2
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