algebra 1 lesson 5-2 warm-up. algebra 1 “slope-intercept form” (5-2) what is “slope- intercept...

of 14 /14
ALGEBRA 1 Lesson 5-2 Warm-Up

Upload: eustace-jacobs

Post on 13-Dec-2015

233 views

Category:

Documents


2 download

TRANSCRIPT

Page 1: ALGEBRA 1 Lesson 5-2 Warm-Up. ALGEBRA 1 “Slope-Intercept Form” (5-2) What is “slope- intercept form” slope-intercept form: a linear equation (forms a

ALGEBRA 1

Lesson 5-2 Warm-Up

Page 2: ALGEBRA 1 Lesson 5-2 Warm-Up. ALGEBRA 1 “Slope-Intercept Form” (5-2) What is “slope- intercept form” slope-intercept form: a linear equation (forms a

ALGEBRA 1

“Slope-Intercept Form” (5-2)

What is “slope-intercept form”

slope-intercept form: a linear equation (forms a line) which include the slope of the line and its y-intercept (where the line crosses the y-axis) – It is written as:

where m (the coefficient of the x term) is the slope and b is the y-intercept (where the line crosses the y-axis)

Page 3: ALGEBRA 1 Lesson 5-2 Warm-Up. ALGEBRA 1 “Slope-Intercept Form” (5-2) What is “slope- intercept form” slope-intercept form: a linear equation (forms a

ALGEBRA 1

The slope is 2 and the y-intercept is –3.

What are the slope and y-intercept of y = 2x – 3?

mx + by =

2x – 3

Use the Slope-Intercept form.

y =

Slope-Intercept FormLESSON 5-2

Additional Examples

Page 4: ALGEBRA 1 Lesson 5-2 Warm-Up. ALGEBRA 1 “Slope-Intercept Form” (5-2) What is “slope- intercept form” slope-intercept form: a linear equation (forms a

ALGEBRA 1

Write an equation of the line with slope and

y-intercept 4.

25

Use the slope-intercept form.y = mx + b

y = x + 425

25Substitute for m and 4 for b.

Slope-Intercept FormLESSON 5-2

Additional Examples

Page 5: ALGEBRA 1 Lesson 5-2 Warm-Up. ALGEBRA 1 “Slope-Intercept Form” (5-2) What is “slope- intercept form” slope-intercept form: a linear equation (forms a

ALGEBRA 1

y = mx + b

Step 2 Write an equation in

slope–intercept form. The y-intercept is 1.

Write an equation for the line.

Step 1 Find the slope. Two points

on the line are (0, 1) and (3, –1).

–1 – 1 3 – 0

slope =

= – 23

23

y = – x + 1

Substitute – for m and 1 for b.

23

Slope-Intercept FormLESSON 5-2

Additional Examples

Page 6: ALGEBRA 1 Lesson 5-2 Warm-Up. ALGEBRA 1 “Slope-Intercept Form” (5-2) What is “slope- intercept form” slope-intercept form: a linear equation (forms a

ALGEBRA 1

“Slope-Intercept Form” (5-2)

How can you determine if a point lies on the line of an equation?

Every point that lies on the graph of an equation must make the equation true. Therefore, to verify (check) whether a point lies on a line, substitute the x and y values of the equation for the x and y coordinates of the point. If the result is a true statement (both sides equal one another), the point is a solution for that equation (in other words, it is part of the graph of that equation).

Example:

Page 7: ALGEBRA 1 Lesson 5-2 Warm-Up. ALGEBRA 1 “Slope-Intercept Form” (5-2) What is “slope- intercept form” slope-intercept form: a linear equation (forms a

ALGEBRA 1

Determine whether (1, 2) lies on the graph of

y = 3x – 1.

y = 3x – 1

2 3(1) – 1 Substitute 1 for x and 2 for y.

2 3 – 1 Multiply.

2 = 2 Subtract.

(1, 2) is a solution.

Slope-Intercept FormLESSON 5-2

Additional Examples

Page 8: ALGEBRA 1 Lesson 5-2 Warm-Up. ALGEBRA 1 “Slope-Intercept Form” (5-2) What is “slope- intercept form” slope-intercept form: a linear equation (forms a

ALGEBRA 1

“Slope-Intercept Form” (5-2)

How do you graph an equation.

There are two ways to graph an equation.

Method 1: Slope-Intercept Form – y = mx + b

Step 1: Start at the y-intercept (0, b)

Step 2: Create a chain of stair-step of the rise (units up or down) and run (units to the right – never to the left since negative slopes go down not left). Place a dot after each step.

Step 3: Connect the dots with a line.

Method 2: Function Table

Step 1: Create a table consisting of 3 colums and at least 3 rows. Label each column “x”, “(equation)”, and “y”

Step 2: Create your own x values and place them in the “x” column (one per row). Tip: Use easy x values to substitute, like 0, 1, 2, -1, and -2.

Step 3: Plot each (x, y) pair.

Step 4: Connect the dots with a line.

Page 9: ALGEBRA 1 Lesson 5-2 Warm-Up. ALGEBRA 1 “Slope-Intercept Form” (5-2) What is “slope- intercept form” slope-intercept form: a linear equation (forms a

ALGEBRA 1

“Slope-Intercept Form” (5-2)

Example: Graph y = -2x + 1.

Method 1: Slope-Intercept Form

Step 1: The y-intercept is 1, so start at (0,1)

Step 2: The slope is -2 or -2/1 which means a rise of -2 (down 2) and a run of 1 (right 1). Create a few stair-steps that go down 2 and right 1.

Step 3: Connect the dots with a line.

Page 10: ALGEBRA 1 Lesson 5-2 Warm-Up. ALGEBRA 1 “Slope-Intercept Form” (5-2) What is “slope- intercept form” slope-intercept form: a linear equation (forms a

ALGEBRA 1

“Slope-Intercept Form” (5-2)

Example: Graph y = -2x + 1.

Method 2: Function Table

Page 11: ALGEBRA 1 Lesson 5-2 Warm-Up. ALGEBRA 1 “Slope-Intercept Form” (5-2) What is “slope- intercept form” slope-intercept form: a linear equation (forms a

ALGEBRA 1

The base pay for a used car salesperson is $300 per

week. The salesperson also earns 15% commission on sales

made. The equation t = 300 + 0.15s relates total earnings t to sales

s. Graph the equation.

Step 1  Identify the slope and y-intercept.

t = 300 + 0.15s

t = 0.15s + 300  Rewrite the equation in slope intercept form.

slope y-intercept

Slope-Intercept FormLESSON 5-2

Additional Examples

Page 12: ALGEBRA 1 Lesson 5-2 Warm-Up. ALGEBRA 1 “Slope-Intercept Form” (5-2) What is “slope- intercept form” slope-intercept form: a linear equation (forms a

ALGEBRA 1

Step 2  Plot two points. First plot a point at the y-intercept. Then use the

slope to plot a second point.

(continued)

Step 3  Draw a line through the points.

15 100

The slope is 0.15, which equals . Plot a second point 15 units above and

100 units to the right of the y-intercept.

Slope-Intercept FormLESSON 5-2

Additional Examples

Page 13: ALGEBRA 1 Lesson 5-2 Warm-Up. ALGEBRA 1 “Slope-Intercept Form” (5-2) What is “slope- intercept form” slope-intercept form: a linear equation (forms a

ALGEBRA 1

m = –2; b = 0

y = 0.5x + 1

34

35

m = ; b = –334

y = – x – 435

Find the slope and y-intercept of each equation.

1. y = x – 3

2. y = –2x

Write an equation of a line with the given slope and y-intercept.

3. m = – , b = –4

4. m = 0.5, b = 1

Slope-Intercept FormLESSON 5-2

Lesson Quiz

Page 14: ALGEBRA 1 Lesson 5-2 Warm-Up. ALGEBRA 1 “Slope-Intercept Form” (5-2) What is “slope- intercept form” slope-intercept form: a linear equation (forms a

ALGEBRA 1

5. Write an equation for the line.

6. Graph y = –x + 3.

y = x – 312

7. Determine whether (3, –7) lies on the graph of y = 4x – 5.

(3, –7) is not a solution

Slope-Intercept FormLESSON 5-2

Lesson Quiz