Slope
Intercepts
Word Problems
y = mx + b
Functions and Relations
100
What kind of slope is between the points (7, 8) and (3, 8)?
What is ZERO SLOPE
100
Find the x and y intercepts of y = x + 5
y- intercept (0, 5) x- intercept (-5, 0)
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
**use a graph*** graph y = -2x + 6
(see graph)
100
Is this relation a function? Tell yes/no and why. {(4, 5), (7, 5), (9, 3), (-2, 10)}
Yes, it's a function. None of the x values repeat. One of the y's repeat, but that's okay.
200
Find the slope of the line that goes between (3, 4) and (4, 6)
What is m = 2
200
Find the x and y intercepts of x - 2y = 8
x intercept (8, 0) y intercept (0, -4)
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 function? Tell yes/no and why. {(-7, 5), (0, 6), (5, 3), (0, 10)}
No-- zero repeats as an x. If there are two x values with different y values, it's not a function.
300
Find the slope of the line that goes between (1, -3) and (5, 4)
What is m = 7/4
300
Find the x an dy intercepts 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
What is the name of the rule that determines whether a relation is a function when you are LOOKING AT A GRAPH?
What is the Vertical Line Test
400
Find the slope of the line that goes between (-3, 6) and (-5, 9)
What is m = -(3/2)
400
We have 48 minutes in class and we will spend time on whiteboard questions and graphs. Each whiteboard question takes 2 minutes and each graph takes 3 minutes. Write an equation for the possible combinations of whiteboard questions and graphs, and then find the x and y intercepts and tell what they mean. (3 answers!)
2x + 3y = 48 x intercept (24, 0) we can do all whiteboard questions (24) and no graphs y intercept (0, 16) we can do no whiteboard questions and 16 graphs
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
Draw an example of a linear function, and an example of a function that is not linear. Label which is which.
(see drawings. Make sure the one that's not linear is still a function!)
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, find the x and y intercepts and tell what they mean.
y = 6x + 18 y intercept: (0, 18) when you get the llama it is already 18 inches tall x intercept (-3, 0) this means that 3 years before you got the llama, it was zero inches tall, which pretty much means that the llama is 3 years old when you get it.
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
Is it possible to have a linear equation that is not a function? Tell yes/no and why.
YES-- you can have a linear equation that is a vertical line. BONUS: give an example of this kind of equation.
M
e
n
u