1. 4.4 The Slope-Intercept Form of the Equation of a Line

2. Slope-Intercept Form
The slope-int. form of an eqn. of a line with slope m and y-intercept b is
y = mx + b
slope y-int
Ex. Find the eqn. of a line with slope 4 and y-int 1.
m = 4, b = 1
y = 4x + 1

3. Ex. Find the slope and y-intercept of y = ¼x – 2
Ex. Find the slope and y-intercept of y = ¼x – 2. y = ¼x – 2 y = ¼x + (-2) m = ¼, b = -2 or (0, -2) Ex. Find the slope and y-intercept of y = -5x. y = -5x + 0 m = -5, b = 0 or (0, 0)

4. Ex. Find the slope and y-intercept of 4x – 2y = 8.
We need to solve for y first (put in slope-int. form y=mx + b)
4x – 2y = 8
4x – 2y – 4x = 8 – 4x
-2y = -4x + 8
y = 2x – 4
m = 2, b = -4

5. Graphing Using Slope and Y-Intercept
y = mx + b
slope y-int: b or (0, b)
Solve the eqn. for y (put in slope-int form)
Plot the y-int. b or (0, b)
Use slope to plot next point
Draw line

6. Ex. Graph y = 2x – 1 using slope and y –intercept.
m = 2, b = -1 or (0, -1)
Plot (0, -1)
Using rise = 2 and run = 1, go up 2 units and right 1 unit to end up at (1, 1) for a 2nd point.
Draw line y 3 2
run= 1 1
rise = 2 x -3 -2 -1 1 2 3 -1 -2 -3

7. Ex. Graph y = -½x using slope and y –intercept.
m = -½, b = 0 or (0, 0)
Plot (0, 0)
Using rise = -1 and run = 2, go down 1 unit and right 2 units to end up at (2, -1) for a 2nd point.
Draw line y 3 2 1 x -3 -2 -1 1 2 3
rise = -1 -1
run = 2 -2 -3

8. Ex. Graph 5x – 3y = 9 using slope and y –intercept.
Solve for y:
5x – 3y = 9
5x – 3y – 5x = 9 – 5x
-3y = -5x + 9
y = 5/3 x – 3
m = 5/3, b = -3 or (0, -3)
Plot (0, -3)
Using rise = 5 and run = 3, go up 5 units and right 3 units to end up at (3, 2) for a 2nd point.
Draw line y 3
run = 3 2 1
rise = 5 x -3 -2 -1 1 2 3 -1 -2 -3

9. Ex. Graph the following lines
Ex. Graph the following lines. Are the lines parallel, perpendicular, or neither? Explain why. y
y = 3x + 1
y = 3x – 3
1) y = 3x + 1
m = 3, b = 1
m = 3, b = -3
The lines are parallel because they have the same slope, but different y-intercepts. 3 2 1 x -3 -2 -1 1 2 3 -1 -2 -3

10. Ex. Write an eqn. in slope-int form (y=mx+b) of the line described:
The y-intercept is -7 and the line is perpendicular to the line
-¼x + y = 5.
Find slope by putting -¼x + y = 5 in slope-int. form.
-¼x + y = 5
-¼x + y + ¼x = 5 + ¼x
y = ¼x + 5
Since m = ¼, the slope of the perp. line is m = -4 (neg. recip.)
Now, b = -7 (given to us) and m = -4 (from step 1) so our line is:
y = mx + b
y = -4x – 7

11. Groups
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