Define the
Word
Word
Rise/run calculates the _________ of a line.
Slope
Identify the slope of the equation y = -x + 6.
The slope is -1
Write the equation of a line where the slope is -9 and the y-intercept is 5.
y = -9x + 5.
Which point lies on the graph of y = 2x - 1?
a. (-2, -4) c. (0, 0)
b. (1, 3) d. (15, 29)
(15, 29)
How can we tell whether a table (or graph) is proportional? There are 2 key details.
(1) the y-intercept is 0 or (0, 0)
(2) All points are scaled in tandem. We can multiply one point to get to another.
10 boxes of cereal weigh 8 pounds. How much does 5 boxes of cereal weigh?
4 pounds
What is 1/2 + 3/4?
5/4
In the equation y = mx + b, what do m and b represent?
m is the slope.
b is the y-intercept.
Find the slope of the points (0, 5) and (2, 10).
5/2
Write the linear equation of the graph.
(see Ms. B's slides)
y = 2x + 4
Graph the equation y = 2x + 4 on your desk. Label the y-intercept and slope on your graph!
Ms. B will check the graph.
Which one of these equations is proportional?
a. y = 3x c. y = 7x - 2
b. y = -4 d. y = 2x + 6
y = 3x since our y-intercept is 0.
At birth, a bird weighs 2 ounces. After 7 days, the bird weighs 18 ounces. Could you find the rate of change? Include units!
slope = 16 / 7 = 2.3 ounces per day.
The shirt costs $25. However, the shirt is on sale for 20% off. What is the new price?
$20
What is another name for slope?
The rate of change.
Identify the slope of the equation y = 14.
The slope is 0.
Write the linear equation of the graph.
(see Ms. B's slides)
y = -2/3x + 5
What is the missing number in the table?
x 0 2 4 6
y -1 1 ? 5
3
Is the table proportional? How do you know?
x 0 2 4 6
y 0 6 12 18
Yes, the table is proportional. The y-intercept is (0,0), and the points are scaled in tandem.
10 boxes of cereal weigh 8 pounds. How many boxes would weigh 12 pounds in total?
15 boxes of cereal
What is 3/4 ÷ 2/5?
15/8
The point (0, 0) is called the _________.
Origin
Find the slope of the points (-2, 8) and (5, -13).
Slope = -21/7 = -3.
Write the equation of a line that passes through the points (4, 19) and (13, 55). The y-intercept is -3.
y = 4x - 3.
Is the point (38, 20) on the line y = 1/2x - 1? How do you know?
No, when you plug in x = 38, you should get 1/2(38) - 1 = 17.
Is the table proportional? How do you know?
x 0 1 2 3
y 12 16 20 24
No, the y-intercept isn't at (0, 0). Also, 1(3) = 3 but 16(3) isn't 48. It's 24 on the table.
This relationship is linear but not proportional.
Which line has the greater slope? How do you know?
(See Ms. B's slides)
The solid line is because the line is more steep. Students can calculate each slope and compare those values too.
What is 5/8 - 1/3?
7/24
In a word problem, the y-intercept represents the _________.
Starting cost or value.
Could you identify the slope of the table below?
x -1 2 5 8
y -2 7 16 25
The slope is 9/3 = 3.
Write the equation of a line that passes through the points (0, 2) and (-4, 5).
y = 3/4x + 2
Which graph is steeper? How do you know?
y = -12x - 13
y = 10x + 15
y = -12x - 13 because the slope is a greater value.
Is the table proportional? How do you know?
x 0 10 20 30
y 0 120 240 330
No, 10(3) = 30. However, 120(3) = 360. In our take, the y-value is 330.
A scoop of ice cream with 2 toppings costs $3.07. A scoop of ice cream with 5 toppings costs $4.75. How much does the ice cream cost with 0 toppings?
x 0 2 5
y ? 3.07 4.75
The cost is $1.95
When we find the slope, each topping costs 0.56 cents. 3.07 - 2(0.56) = $1.95.
You buy a computer for $800. You pay an 8% sales tax. How much do you pay in total?
You will pay $864.