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determine if the lines that pass through the given points are parallel, perpendicular or neither. line a: (2, 3) and , 5) line b: (-4, 9) and (-3, 12)
after 3 hours of waiting tables, jerome made $25 in tips. after 8 hours of waiting tables, jerome made $115 dollars in tips. find the average rate of change of dollars per hour.
find the rate of change between the two points (1, 6.2) and (3, 20) where x is in hours and y is in miles.
write the equation of a line that passes through the points ( -2, 5) and (-2, 11).
shelly has $250 in her savings account. she spends $30 per week. describe the slope in this situation.
the tow truck company charges $95 plus an additional $0.30 per mile. if your total bill was $101.60, how many miles did the tow truck take you?

1)
We have to find the slope of these lines;
Given two points (x₁,y₁) and (x₂,y₂) ; the slope would be:
m=(y₂-y₁)/(x₂-x₁)
Line 1: (2,3) and (-4,5) ⇒ m=(5-3)/(-4-2)=2/-6=-1/3.
Line 2: (-4,9) and (-3,12) ⇒ m=(12-9)/(-3+4)=3

m and m´are perpendicular if m=-1/m

In this case: 3=-1/(-1/3); therefore these lines are perpendicular.

the lines are perpendicular.

2)
We have two points: (3,25) and (8,115); the average rate of change of dollars per hour, would be the slope of the line passes through these points.
m=(y₂-y₁)/(x₂-x₁)
m=(115-25)/(8-3)=90/5=18

the average rate of  change would be 18 dollar/hour.

3)
We have two points: (1, 6.2) and (3 , 20); the  rate of change of miles per hour, would be the slope of the line passes through these points.
m=(y₂-y₁)/(x₂-x₁)
m=(20-6.2)/(3-1)=13.8/2=6.9

The rate of change would be 6.9 miles/ hour.

4)
1) We have to compute the slope of the line passes through these points.
m=(y₂-y₁)/(x₂-x₁)
m=(11-5)/(-2+2)=6/0; because the denominator is equal to zero, we have a perpendicula line.
 In this case  we  can look at one point  (x₀,y₀), then the equation  of the line would be: x=x₀;
We choose one point, for example : (-2,5), then the equation of the line will be x=-2

the equation of the line would be x=-2.

5)
slope-intercept form:
y=mx+b
m=slope

In this case:

y=money of Shelly
x=number of weeks

y=-30x+250

The slope would be m=-30.

the slope would be m=-30.

6)
We have the following equation:
y=0.3x+95
y=total money charged
x=number of miles.

We have the following information:
y=101.6

Then:
101.6=0.3x+95
0.3x+95=101.6
0.3x=101.6-95
0.3x=6.6
x=6.6/0.3
x=22

22 miles