Warm-up: Investigation
1. Graph the following equations using a table of values.
a) y=3x
b) y=2x
c) y=-5x
Find the slope of each line.
What do you notice? (They should see that the slope is equal to the number in front of the x)
2. Graph the following equations using a table of values:
a) y=2x
b) y=2x+1
c) y=2x-3
Without calculating, what is the slope of these lines? Look at where the lines cross the y axis. What do you notice? (They should see that they cross the y axis at 0, 1, -3 – same #s in equations)
Lesson 2-4b: Graph a Line using Slope and Y-intercept
Example 1:
The equation y = 2x + 3 is written in the slope y-intercept form.
m is the slope of the line
b is the y-intercept (point where the line crosses the y axis, or where x=0)
In our example, the slope is 2 and the y-intercept is 3. Using this information, we can now graph the line:
Step 1: Plot y-intercept (0,3).
Step 2: Use slope to find another point (rise 2, run 1) at (1,5). *Should graph 3rd point at (2,7) or (-1,1).
Step 3: Draw line.
Example 2:
State the slope and y-intercept for the line represented by the equation:
a) y=-3x-5 b) y= ½x+8 c) y= -¾x+12
(Answers: a) m=-3, b=-5 b) m= ½ ,b=8 c) m = -¾ , b=12)
Example 3:
Write the equation of each line given the slope and y-intercept:
a) m=2, b=-3 b) m= -¼, b=½
(Answers: a) y=2x-3 b) y= -¼x + ½ )
Example 4:
State the slope, y-intercept and the equation of the line:
y-intercept is 2 so b=2
slope = rise
run
= -4
2
=-2
So m=-2
Equation is
y = -2x + 2
Classwork/Homework: p. 110 #1aceg, 2ace, 3, 4a, 5a parts i, iii, v, vii