Calculate Slope
Standard Form
Linear Relationships
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Random
100
(5, 7) and (3, 6)
What is 1/2?
100
Rewrite y=2x+3 in standard form.
−2x+y=3
make A positive:
2x−y=−3
100
Points: (1, 2), (2, 4), (3, 8), (4, 16)
Do these points form a linear function?
Explain
No, not linear.
The y-values are doubling (exponential), not increasing by a constant amount.
100
What is the measure of the steepness of a line?
What is Slope?
100
Simply
(5x+2y−7) − (3x−4y+5)
Then turn to Slope intercept
2x + 6y – 12
y= − 1/3x + 2
200
(2, 5) and (8, 1)
What is -2/3?
200
Rewrite 9x + 6y = –12 in slope-intercept form. Then state the slope and y-intercept.
y = −3/2x − 2
✅ Slope: –3/2 Y-intercept: –2
200
Identify the slope and y-intercept in the equation y=−2x+5
What is
Slope = -2, Y-intercept = 5
200
What part of the graph is the steepest?
How Steep (in meteres)?
The steepest section is from 140 seconds to 160 seconds?
From 0 to 20 seconds, the distance increases from 0 to 30 meters.
From 20 to 60 seconds, the distance stays constant at 30 meters.
From 60 to 100 seconds, the distance increases again from 30 to 50 meters.
From 100 to 140 seconds, it remains at 50 meters.
From 140 to 160 seconds, it drops sharply from 50 to 0 meters.
200
Who is the greatest Superhero of all time?
Batman
300
y = -3x - 2
What is -3?
300
Rewrite 8x – 4y = 12 in slope-intercept form. Then state the slope and y-intercept.
What is
y = 2x−3
Slope: 2 Y-intercept: –3
300
Answer: B, C, E, and F
300
How do you find slope on a graph?
What is Rise over Run?
300
Question:
Ava and Marcus both made salt water to help with their sore throats.
Ava mixed 3 teaspoons of salt with 6 cups of water.
Marcus mixed 5 teaspoons of salt with 12 cups of water.
After trying each other’s mixtures, Marcus said:
“I added more salt and more water, but mine still doesn’t taste the same as yours!”
Part A:
Explain why the salt water mixtures are different.
Part B:
Write an equation that relates sss (salt in teaspoons) to www (water in cups) for both mixtures.
The mixtures are different because the ratios of salt to water are not equal.
Ava’s ratio: 3/6 = 1/2 (0.5)
Marcus's ratio: 5/12 or 0.42
Ava: s = 1/2w
Marcus: s = 5/12w
400
4x + y = 7
What is -4?
400
Rewrite y = –2.5x + 10 in standard form using integers.
2.5x + y = 10
Multiply through by 2 to remove the decimal:
2y=−5x+20
5x+2y=20
400
Which of the following equations represents a line with a zero slope?
A. x=4
B. y=7
C. y=−x
D. y=2x+3
What is B?
y=7
a horizontal line.
400
The function below represents a relationship between x and y.
(0,2), (2,8), (4,14)
Which function has a greater rate of change than the one represented by these points?
A. y = 4x+3
B. 4y − x = 8
C. y = 3x+1
D. 2y=3x
The slope (rate of change) is 3.
A. y = 4x+3
400
What is the greatest Disney movie ever?
Toy Story
500
-6x + 3y = 9
What is 2?
500
Rewrite 2.5x – 0.5y = 3 in slope-intercept form. Then state the slope and y-intercept.
-0.5y = 2.5x + 3
y = 5x − 6
Slope: 5 Y-intercept: –6
500
Select All That Apply
❏ A. The puppy’s weight increases at a constant rate of 1 lb per week.
❏ B. The puppy’s weight increases at a constant rate of 2 lb per week.
❏ C. The puppy’s weight increases at a constant rate of 4 lb per week.
❏ D. The initial weight of the puppy was 7 lb.
❏ E. The initial weight of the puppy was 9 lb.
What is B?
Step 1: Find the rate of change (slope)
m=13−9= 4 4-2=2.
4/2= 2
So the slope = 2 lb per week
Step 2: Find the initial weight (y-intercept)
Using point (2, 9):
9=2(2)+b ⇒ b=5
That means when the puppy was 0 weeks old, it weighed 5 pounds.
500
All of the points below lie on the same line.
(2,5), (c,11), (8,17)
What is the value of c?
A. 3
B. 4
C. 5
D. 6
m=2
y = 2x + b
Plug in (2,5)
y=2x+1
Plug in 11
What is C?
500
Part A: What is the unit rate at which the pool was being filled?
Part B: How much water was in the pool before it started being filled?
Part C: Write an equation that relates the number of gallons of water, www, to the time in minutes, t.
Then explain how you would use the equation to find how long it will take to reach 600 gallons.
The pool is being filled at a rate of 8 gallons per minute.
180 = 8(15) + b
b = 60
w=8t+60
t= 67.5