MAT 101 Selected Problems Worksheet
Name: __________________________
Questions: (Fill in every blank!)
The length of a rectangle is 2 feet less than seven times its width. The
perimeter is 92 feet. Find the length of the rectangle.
width = W
Write an expression for Length using W
Length = ____________
The perimeter formula is: P = 2( L + W) so
P = 2(
L
+ W)
P = 2( ___________ + W) (Substitute for L using the expression. )
P = ___ W + _____ + 2W
(Distribute)
(Use perimeter # from problem & Combine like terms.)
so
P
______ = __________ + __________
Now solve your equation for W.
____________ = W
Answers:
W = _____ feet
Go back and use what you just got for W to find L.
(look up)
So L = _______
Final answer:
L = _____ feet
Finding the Slope of a Line
Find the slope of a line containing any two given points:
slope = m =
y 2  y1
x2  x1
a. A line with a negative slope (m < 0) falls as you go from left to right.
Example: Given two points: (3,0) and (-2, 1)
y  y1
1 0
1
m= 2
=
=
23 5
x2  x1
The slope of the line containing (3,0) and (-2, 1) is
-1.
5
b. A line with a positive slope (m > 0) rises as you go from left to right.
Example: Given two points: (-3,0) and (2, 1)
y  y1
1 0 1
m= 2
=
=
2  3 5
x2  x1
The slope of the line containing (-3,0) and (2, 1) is
1
.
5
c. A line with an undefined slope is vertical.
Example: Given two points: (3,3) and (3, 1)
NOTE: Both x values are the same! The equation of this line is x =3!
y  y1
1 3  2
m= 2
=
=
= undefined,
33
0
x2  x1
since division by zero is undefined.
The slope of the vertical line containing (3,3) and (3, 1) is undefined.
d. A line with a zero slope (m = 0) is horizontal.
Example: Given two points: (1,2) and (5,2)
NOTE: Both y values are the same! The equation of this line is y =2!
y  y1
22 0
m= 2
=
= =0
5 1 4
x2  x1
The slope of the horizontal line containing (1,2) and (5,2) is 0.
The Point-Slope Form of the Equation of the Line
When you know the slope of a line and the coordinates of at least one point on the
line, you can find the equation of the line.
(x, y) ●
y- y 1
(x 1 , y 1 )
●
Consider the slope formula.
x - x1
y  y1
m=
Multiply both sides of this equation by the denominator.
x  x1
The point slope form of the equation of the line that passes through the point (x 1 , y 1 )
and has slope m is y - y 1 = m (x - x 1 ) .
Find an equation of the line that passes through the point (1, -3) and has slope 2.
y - y 1 = m (x - x 1 )
y - ___ = ___ (x – ___)
Substitute for y1, m, and x1.
y + 3 = 2x - 2
Distribute. Remember that subtract means add the opposite.
y + 3 ____ = 2x – 2 ____ Subtract the same thing from both sides to isolate y.
y = 2x - 5
Simplify.