Drill #21A. Write each equation in Standard Form.

B. Identify A, B, and C

C. Find the x- and y- intercepts

D. Graph each equation using the intercepts

3

5

2

5.3

6

5

4

3

3

1.2

42186.1

yyx

xy

xy

Drill #22Write the following equation in a.) Standard Form.

b.) Identify the slope and x- and y- intercepts. c.) use the intercepts to graph the line.

Find the value of r so that the line that passes

through each pair of points has the given slope:

2

26

3

3.1

yyx

54

)7,7(,)1,(.3

2

1),7(),2,3(.2

mr

mr

2-3 Slope and Rate of Change

Objective: To find the rate of change, to determine the slope of a line, and to use the slope and y-intercept to find the slope intercept form of a line.

Slope Intercept Form

The slope intercept form of a line is:

y = mx + b,

Where m = slope and b = y-intercept

Standard Form Formulas

If an equation is in standard form

Ax + By = C

Then

X- intercept = C/A

Y- Intercept = C/B

Slope = -A/B

Slope

The formula for slope given two points is

12

12

xx

yym

Find the slope and y-intercept

Find the slope and y-intercept

Find the slope and y-intercept

Find the slope and y-intercept

Find the value of r…

Graphing Linear Equations

Standard Form:

• Find the x- and y- intercepts

Slope-Intercept Form:

• Use the slope and the y- intercept

Graphing (Slope Intercept)

Steps for graphing an equation in slope-intercept form:

1. Plot b (the y- intercept)

2. Use the slope to find a second point

3. Connect the points and draw a line

Example:

• Graph the following equation that is in slope intercept form:

y = 2x – 2

What is the slope?

What is the y- intercept?

Write the equation of a line:

x

y

-4

2

Classwork

Identify the equations in 2-3 Skills Practice #10-15

A plane descends at a rate of 1000 ft per second. If it starts at 10,000 ft,

a.Write an equation to describe the situation

b.What altitude will the plane be at after 8 minutes?

Rate Word Problems

Rate Word Problems

A plane ascends at a rate of 1500 ft per second. If it starts at 2,000 ft,

a.) Write an equation to describe the situation

b.) What altitude will the plane be at after 8 minutes?

Slope*

Slope: The ratio of the change in vertical units to the change in horizontal units (RISE OVER RUN).

The formula for the slope m of the line passing through and

is given by .

That is the change in the y coordinate (RISE) over the change in the x coordinate (RUN)

),( 11 yx ),( 22 yx

12

12

xx

yym

Point Slope FormDefinition: An equation in the form of

where

Are the coordinates of a point on the line and m is the slope of the line.

NOTE: For point slope form we need a point and the slope (or two points).

)( 11 xxmyy ),( 11 yx