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.
Answer: 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
Answer: 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
Answer: 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
Answer: 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.
Answer: 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
Answer: 22 miles
