4. of a line containing two points with
coordinates (x1, y1) and (x2, y2) is
given by the formula
y
y
2 1
x x
2 1
m
5. Slopes
y
y
2 1
x x
2 1
m
5
5
1 3
All horizontal
lines have a 0
slope
All vertical lines
have an
undefined
slope
0
0
4
y
y
2 1
x x
2 1
m
4 3
6 6
7
undefined
0
6. Rise (upward) as you move left to right
Line slopes
up from left
to right
y
x
7. Fall (downward) as you move left to right
Line slopes
down from
left to right
y
x
8. Find the slope using the
slope formula.
y
y
2 1
x x
2 1
m
7
8
5 2
2 6
7
8
y
y
2 1
x x
2 1
m
0
1
4 0
1
4
1
4
9. Describes how a quantity is changing over
time.
The slope of a line can be used to
determine the Rate of Change
y
x
Change in quantity (y)
Change in time (x)
10. Recreation: For one manufacturer of camping equipment,
between 1990 and 2000 annual sales increased by $7.4 million
per year. In 2000, the total sales were $85.9 million. If the
sales increase at the same rate, what will be the total sales in
2010?
y
y
2 1
x x
2 1
m
7.4
1
y
85.9 2
2010 2000
85.9
7.4 2
10
1
y
7.4(10) = y2 – 85.9
74.0 = y2 – 85.9
+85.9 +85.9
159.9 mill. = y2
11. Slope-Intercept Form -
y = mx + b
slope y-intercept
Point-Slope Form -
y – y1 = m(x – x1)
y-coordinate slope x-coordinate
12. 1
2
y x
3
1
2
y x
3
1.) The equation is in slope-intercept form y = mx + b
2
3
The slope is
y-intercept (0, 1)
2.) Plot the point (0, 1)
2
3.) Use the slope , from
3
the point (0, 1) go up 2,
right 3
13. y 3x 1
1.) The equation is in slope-intercept form y = mx + b
1
2
y x
3
The slope is 3
y-intercept (0, 1)
2.) Plot the point (0, 1)
3.) Use the slope 3, from
the point (0, 1) go up 3,
right 1
14. 1.) The equation is in point-slope form y – y1 = m(x – x1)
The slope is -2
Point on line (-3, 3)
2.) Plot the point (-3, 3)
3.) Use the slope -2, from
the point (-3, 3) go
down 2, right 1
15. 1
y 2 x
( 4)
3
1.) The equation is in point-slope form y – y1 = m(x – x1)
1
The slope is
3
Point on line (4, 2)
2.) Plot the point (4, 2)
1
3.) Use the slope , from
3
the point (4, 2) go
down 1, right 3
16. If we know the slope and at least one point
If we have the slope and y-intercept, use the
slope-intercept form; y = mx + b
If we have the slope and a point, use the
point-slope form; y – y1 = m(x – x1)
17. What is an equation of the line with slope 3
and y-intercept -5?
Start with the slope-intercept form of
the equation
y = mx + b
y = 3x + (-5) Substitute 3 for m, and -5
for b
y = 3x - 5 Simplify
18. What is an equation of the line through point
(-1, 5) with slope 2?
Start with the point-slope form of the
equation
y – y1 = m(x – x1)
y – 5 = 2(x - (-1)) Substitute 2 for m, and -1
in for x1 and 5 in for y1
y – 5 = 2(x + 1) Simplify
19. What is an equation of the line with
1
slope and y-intercept 2?
2
Start with the slope-intercept form of
the equation
y = mx + b
1
1
y = x + 2
Substitute for m, and
2 for b 2
2
20. What is an equation of the line through point
(-1, 4) with slope -3?
Start with the point-slope form of the
equation
y – y1 = m(x – x1)
y – 4 = -3(x - (-1)) Substitute -3 for m, and -1
in for x1 and 4 in for y1
y – 4 = -3(x + 1) Simplify
21. If we know two points on the line
Find the slope using the formula
Using the point-slope formula
Plug in one of the two points
Plug in the slope for m
22. What is an equation of the line through point (-2, -1)
and point (3, 5)?
y
y
2 1
x x
2 1
m
Find the slope
6
y + 1 = (x + 2) or
5
6
5 1
6
6
y - 3 = (x - 5)
5
3 2
5
5
Start with the point-slope form of the equation
y – y1 = m(x – x1)
Plug in the slope and one of the two points
23. We don’t need a slope
All points on a horizontal line have the
same y-coordinate; so the equation is y = y1.
All points on a vertical line have the same
x-coordinate; so the equation is x = x1.
Where (x1, y1)
24. What are the equations for the horizontal and
vertical lines through (2, 4)?
The horizontal is y = y1
y = 4 Substitute 4 for y1
The vertical is x = x1
x = 2 Substitute 2 for x1
25. What are the equations for the horizontal and
vertical lines through (4, -3)?
The horizontal is y = y1
y = -3 Substitute -3 for y1
The vertical is x = x1
x = 4 Substitute 4 for x1
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