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DSPM 0800 HOMEWORK (ASSIGNMENT 7, SECTIONS 9-3 THROUGH 9-4)
Find the slope of the line passing through the pairs of points:
- (-1, -1) and (3, 6)
The slope of a line is computed by using the slope formula. It does not matter which point is point 1 and which is point 2. Make sure you substitute correctly.
2 1
2 1
1 2 1 2
7 4
y y m x x
x x y y
2 1
2 1
7 4 7 4
y y m x x
- (3, -4) and (0, 0)
2 1
2 1
4 3 4 3
y y m x x
2 1
2 1
4 3 4 3
y y m x x
- (3, 3) and (3, 0)
2 1
2 1
3 0
y y m x x
2 1
2 1
3 0
y y m x x
Since the slope has zero in the denominator, the line is a vertical line. The slope is undefined.
- (3, 1) and (5, 7)
2 1
2 1
6 2
y y m x x
2 1
2 1
6 2
y y m x x
- In 1995 the sales of airplanes totaled $1,400,000. Eleven years later (2006) the sales
totaled $3,900,000. Find the average annual rate of change in the sales of airplanes, to
the nearest dollar.
2 1
2 1
2,500, 11
y y m x x
The average annual rate of change is about $ 227,.
Find the equation of a line passing through the given point with the given slope:
m
Use the point-slope formula, y^ ^ y 1^ ^ m x (^^ ^ x 1 ).
1 1 1 3 1 1 1 3 1 3 1 3 1 3 1 3
y y m x x m x y
y x
y x
y x
y x
y x
- (6, 0), m = -
1 (^1 )
y y m x x
y x
y x
m
1 1 2 5 2 5 2 5 2 5
y y m x x
y x
y x
y x
y x
Find the equation of a line passing through the given pair of points:
- (-5, -6) and (4, 5)
Compute the slope first, then use either point in the point-slope formula.
2 1
2 1
11 9
y y m x x
2 1
2 1
11 9 11 9
y y m x x
1 1 11 9 11 44 9 9 11 44 9 9 11 44 45 9 9 9 11 1 9 9
y y m x x
y x
y x
y x
y x
y x
1 1 11 9 11 9 11 55 9 9 11 55 9 9 11 55 54 9 9 9 11 1 9 9
y y m x x
y x
y x
y x
y x
y x
y x
- (-1, -2) and (-3, -4)
2 1
2 1
2 2
y y m x x
2 1
2 1
2 2
y y m x x
1 (^1 )
y y m x x
y x
y x
y x
y x
y x
1 (^1 )
y y m x x
y x
y x
y x
y x
y x
1 1
1 2
4 (Put in slope-intercept form; 1)
5 1( 2) (Substitute 1, 2, 5)
5 2
2 5
7 (
x y
x y x x
y x m
y y m x x
y x m x x
y x
y x
y x
In slope-intercept form)
If you wish to put the equation in standard form (^ ax^ ^ by^ c^ ), rearrange so that the x and y terms are on the same side of the equation:
x y x x
x y
- The line parallel to x^ ^3 y ^5 through (5, -5)
1 5 1 1 3 3 3 3
1 1 1 3 1 5 3 3 1 5 3 3 1 5 15 3 3 3 1 20 3 3
(Slope is , slope of parallel line is )
x y
x y x x
y x
y x
y y m x x
y x
y x
y x
y x
y x
To find standard form, clear fractions:
1 20 3 3( 3 ) 3( 3 )
3 20
3 20
3 20 or 3 20 (Some require that not be negative)
y x
y x
x y x x
x y x y a
- The line parallel to ^2 x^ ^3 y ^2 through (-1, -1)
2 2 2 2 3 3 3 3
1 1 2 3 2 3 2 2 3 3 2 2 3 3 2 2 3 3 3 3 2 1 3 3
(Slope is , slope of parallel line is )
x y
x y x x
y x
y x
y y m x x
y x
y x
y x
y x
y x
y x
2 1 3 3( 3 ) 3( ) 3
3 2 1
2 3 2 1 2
2 3 1 or 2 3 1
y x
y x
x y x x
x y x y
- The line perpendicular to 5 x^ ^ y ^8 through (-1, 2)
Perpendicular lines have slopes that are negative reciprocals of each other. Compute the slope of the given line, take its reciprocal, then reverse the sign.
x y
x y x x
y x
The negative reciprocal of -5 is
1
- Therefore, the slope of the perpendicular line
is
1
