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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)
y = 2 x +3
a)
b)
y=
−2
x−5
3
Things to think about:
1) Could you tell that the graph of y = 2 x +3 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 y = 2 x +3 ?
3) Which of the following points are on the line represented by the equation y = 2 x +3 ?
(10, 23)
(1.5, 5)
(5, 12)
Use your graphs to complete the table:
Equation
y = 2 x +3
y=
Slope
y-intercept
(200, 403)
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
−2
x−5
3
What do you notice? ________________________________________________________________
Math 10
Ch 7. Linear Equations and Graphs
The Equation of a Line (in slope-intercept form):
Ex. #1 Write the equation of each line in slope-intercept form.
Ex. #2 Complete the table below:
Equation
Slope
y-intercept
−3
5
57
71
33
y = 5 x +2
3
y = − x−5
7
y = 2x
Lesson 7-1
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)
y=
2
x +1
3
b)
y = −3x − 4
Ex. #4 Find the slope and y-intercept of the following lines:
a) 2 x + 3 y = 9
Ex. #5
a)
b)
b) 4 x − 8 y − 15 = 0
Point C(-2,-6) is on the line y = 2 x + b . Find the y-intercept of the line.
Point D(4,-5) is on the line y = mx + 5 . 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 ________________
Domain ________________
dependent variable __________________
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?