Math 10 Ch 7. Linear Equations and Graphs Lesson 7-1 Lesson 7-1 Slope-Intercept Form Investigate: Graph the following lines using a table of values: (Hint: for part b you may find it easier to choose “x” values that are multiples of 3)

a) 2 3y x b) 2

53

y x

Things to think about:

1) Could you tell that the graph of 2 3y x would form a line before you started graphing it? How?

2) How could you tell if the point (-5, -7) is on the line represented by the equation 2 3y x ?

3) Which of the following points are on the line represented by the equation 2 3y x ?

(10, 23) (1.5, 5) (5, 12) (200, 403)

Use your graphs to complete the table:

Equation

Slope

y-intercept

2 3y x

25

3y x

What do you notice? ________________________________________________________________

y-intercept: - the y-coordinate where the graph of a

line or function crosses (intersects) the y axis.

- The value of y when x=0

Math 10 Ch 7. Linear Equations and Graphs Lesson 7-1 Ex. #1 Write the equation of each line in slope-intercept form. Ex. #2 Complete the table below:

Equation Slope y-intercept

5 2y x

35

7y x

3 5

57

71

33

2y x

The Equation of a Line (in slope-intercept form):

Math 10 Ch 7. Linear Equations and Graphs Lesson 7-1 Ex. #3 Graph each of the following lines without using a table of values. Check your work with a graphing calculator:

a) 2

13

y x b) 3 4y x

Ex. #4 Find the slope and y-intercept of the following lines:

a) 2 3 9x y b) 4 8 15 0x y

Ex. #5 a) Point C(-2,-6) is on the line 2y x b . Find the y-intercept of the line.

b) Point D(4,-5) is on the line 5y mx . Find the slope of the line.

Math 10 Ch 7. Linear Equations and Graphs Lesson 7-1 Ex. #6 Student Council decides to hold a dinner-dance. The cost to decorate the gym, rent the dishes and sound

equipment and to print the posters advertising the event is $475. Dinner costs $20 per person. a) Graph the cost of the event against the number of people who attend. The gym can hold a maximum of 400

people.

b) For your graph, identify the: independent variable ________________ dependent variable __________________ Domain ________________ Range _______________ Does this graph represent a function? _______ (how do you know?)

c) Write an equation to represent the cost of hosting the dance. Let C represent the total cost and n the number

of students who attend.

d) What does the slope represent? the y-intercept?