Section 6-: Point-slope Form of a Linear EquationSPI 22C: select the graph that represents a given linear function

Objective: Graph and write linear equations in point-slope form

1. Slope-Intercept form: y = mx + b2. Standard Form: Ax + By = C3. Point-Slope form: y – y1 = m (x – x1)

3 Different Forms of a Linear Equation

y – y1 = m ( x – x1)

Point-Slope Form of a Linear Equation

one set of ordered pair another set of ordered pair

Slope of the linear equation

Graph the equation y – 2 = (x – 1).

Step 2. Write the slope (m).

Graph a Linear Equation in Point-Slope Form

13

y – y1 = m (x – x1)

(2, 1)

Step 1. Write the (x, y) ordered pair.

13

Step 3. Graph the equation• plot ordered pair first• use slope from known point• draw solution line

y – = (x – )

Write the equation of a line with slope -3 that passes

through the point (-1, 7).

Write a Linear Equation in Point-Slope Form

y – y1 = m (x – x1)

What is the slope in the problem? -3

-3

What is the point in the problem? (-1, 7)

(-1)7

Simplify y – 7 = -3(x + 1)

Write an equation for the line in point-

slope form.

Use Two Points to Write an Equation (Point-slope Form)

y – y1 = m (x – x1)

Step 1. Locate any two points

(-1, 4) and (2, 3)

Step 3. Use either point to write an equation.

Step 2. Use the points to find the slope

12

12

xx

yym

3

1

3

1

21

34

m

))1((3

14 xy )1(

3

14 xySimplify

Write an Equation using a Table

x Y

-1 4

3 6

5 7

11 10

Is the relationship shown in the table linear? If so, model the data with an equation.

Step 1. Find the rate of change of consecutive ordered pairs. (If the rate of change is the same, then the data is linear).

3 – (-1) = 4

5 – 3 = 2

11 – 5 = 6

6 – 4 = 2

7 – 6 = 1

10 – 7 = 3

Rate of Change

Change in yChange in x

24

= 12

12

= 12

36

= 12

Rate of change is the same, so the data is linear

Continued . . . .

x y

-1 4

3 6

5 7

11 10

Is the relationship shown in the table linear? If so, model the data with an equation.

Step 2. Model the data with an equation Recall: Rate of change (slope) is ½ .

12

y – y1 = m (x – x1)

y – = (x – )

Use any ordered pair, from the table, to complete the equation

57

y – = (x – )

Real-world and Tables of Data

Temperature Calories

68° 3030

62° 3130

56° 3230

50° 3330

The table at the right represents the amount of calories burned per day when working outdoors at the stated temperature.

Is the relationship shown in the table linear? If so, model the data with an equation in point slope form.

Step 1. Is the data linear? If so, what is the rate of change? 3

50

Step 2. Write an equation in point-slope form.

503330 3

50