Do Now 1. Solve the equation 2. Find the x-intercept and the y-intercept of the equation +4x 2 + 5x = x = x = -2 5x + (0) = 25 5x = 25 x = 5 (5,0) 5(0) + y = 25 y = 25 (0,25)

 Section 5.1 Slope-Intercept Form y = mx + b

 Important!!! This is one of the big concepts in Algebra 1. You need to thoroughly understand this! Slope – Intercept Form y = mx + b m 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 = m x + b m = 3, b = (0,-7)

Find the slope and y-intercept. 2) y = x y = m x + b y = x + 0 3)y = 5 y = m x + b y = 0x + 5 m = b = (0,0) m = 0 b = (0,5) HORIZONTAL LINE

-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 - 2 m = b = (0,-2)

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 22 m = 2 b = (0,-1)

Find the slope and y-intercept of y = -2x m = 2; b = 4 2. m = 4; b = 2 3. m = -2; b = 4 4. m = 4; b = -2

Convert Into Slope-Intercept Form (divide both sides by 2 to get y alone) (now simplify all fractions) 21

When an equation is in slope-intercept form: What is the slope? ____________ Now look at the equation below…… What is the intercept? ____________

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 + 15 Convert to Slope-Intercept Form: (divide both sides by 5 to get y alone) (now simplify all fractions) y = 2x + 3 BRAVO!!

*** 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 y = -9x Slope = 3 Intercept = 4 Wow, you’re good at this!!

*** medium *** 21x – 7y =14 Convert to Slope-Intercept Form: (subtract both sides by 21x) -7y = -21x + 14 (now divide both sides by -7) y = 3x – 2 (simplify all fractions)

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 ***

Slope-Intercept From y = 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)

Example 4-1c Ex 1Write 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

Example 4-2d Ex 2Write 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 = 3 y-intercept = (0,-6) 2. Slope = -2 y-intercept = (0,7) 3. Slope = 2/5 y-intercept = (0,-10)

Write the equation of a line that has a y-intercept of -3 and a slope of y = -3x – 4 2. y = -4x – 3 3. y = -3x y = -4x + 3

Now look at this graph and create the equation m = -2/1 b = (0,2)

Now look at this graph and create the equation m = 1/1 b = (0,2)

Now look at this graph and create the equation m = -4/1 b = (0,0)

Now look at this graph and create the equation m = 2/3 b = (0,-3)

Now look at this graph and create the equation m = undefined b = none

Now look at this graph and create the equation m = none b = (0,-2)

Write an equation given two points on a graph b = (0,-3) m = y = x - 3 x y +2 +3

Example 2 b = (0,1) m = y = x + 1 x y 2

Example 3 b = (0,4) m = 0/1= 0 y = 0x + 4, y = 4 x y

Write an equation of a line A B C

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 + b y = 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