Slope
Intercepts
Word Problems
y = mx + b
Proportional and Nonproportional Relationships
100
What kind of slope is between the points (7, 8) and (3, 8)?
What is ZERO SLOPE
100
Determine the y-intercept of y = x + 5
The y-intercept is 5
100
Jasmine has $18 to buy books at the library used book sale. Paperback books cost $3 each. Write an equation to show her amount of money left (y) based on how many books shy buys (x)
y = -3x + 18
100
Graph y = -2x + 6
(see graph)
100
Is this relation proportional? Tell yes/no and why.
Yes, it's proportional, it changes at a constant rate and goes through the point (0,0)
200
Find the slope of the line that goes between (3, 4) and (4, 6)
What is m = 2
200
Determine the y-intercept
The y-intercept is 1
200
The perimeter of a rectangle is 50 inches. Write an equation to find possible lengths and widths of the rectangle.
2x + 2y = 50
200
write an equation of a line that has a slope of -3 and a y-intercept of 5
y = -3x + 5
200
Is this relation a proportional relationship?
No, it has a constant rate of change, but does not go through the point (0,0)
300
Find the slope of the line that goes between (1, -3) and (5, 4)
What is m = 7/4
300
Determine the y intercept of 6x + 7y = 12
x intercept (2, 0) y intercept (0, 1 and 5/7)
300
A roller coaster drops down 56 feet as its track goes 42 feet forward. What is the slope of the drop?
m = -4/3
300
write an equation of a line that goes through (5, 8) and (9, 12) and has a y intercept of (0, -8)
y = x - 8
(use the points to find the slope, then plug it all in)
300
How do you determine if a relationship is proportional or not?
It must have a constant rate of change and go through the origin point (0,0)
400
Find the slope of the line that goes between (-3, 6) and (-5, 9)
What is m = -(3/2)
400
Determine the y-intercept
The y-intercept is -5
400
You are predicting how much money you will have saved (y) after working a certain number of hours (x). You use the equation y = 18x + 500. How much do you already have saved and how much do you earn per hour? How much will you have after working a full work week (40 hours)? ***THREE ANSWERS***
-already saved $500
-earn $18 per hour
-after working 40 hours, saved $1220
400
write an equation of a line that has a slope of (-1/2) and goes through the point (2, -5)
y = (-1/2)x - 4
(plug in the slope, then plug in x and y from the ordered pair and solve for b)
400
Does the table show a proportional relationship?
Yes, it has a constant rate of change and the table would contain the point (0,0)
500
Find the slope of the line that goes between (3 and 1/2, 5 and 1/4) and (2 and 1/2, 6) ***use fractions, not decimals, to get the points!
What is m = -3/4
500
You get an 18 inch tall baby llama for your birthday, and the llama guy tells you that it will grow 6 inches per year. Write an equation for how tall the llama will be (y) based on how many years (x) you own it. THEN, fins the y-intercept and tell what it means.
y = 6x + 18 y-intercept: (0, 18) when you get the llama it is already 18 inches tall
500
You take a hot-air balloon ride on a day when the temp is 24 degrees C at sea level. The equation y = -6.6x + 24 represents the temperature (y) at x kilometers above sea level.
-how does the temp change with each km?
-find the x and y intercepts and tell what they mean.
-temp drops 6.6 degrees C with each km you go up
-y intercept (0, 24) when you start at sea level, temp is 24
-x intercept (3.6, 0) when you get up to 3.6 km the temperature drops down to 0 degrees C
500
find the y = mx + b equation for a line that has an x intercept of -3 and a y intercept of 5.
HINT: (-3, 0) (0, 5)
y = (5/3)x + 5
500
Does the table show a proportional relationship?
No, it does not have a constant rate of change