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the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
Check the procedures in the picture attached.
1. Since we are using direct substitution, the only thing we need to do is replace
by 
(the quantity is approaching to) in our quantity to get:
We can conclude that the correct answer is B) -6
2. Again, since we are using direct substitution, th only thing we need to do is replace by 
(the quantity x is approaching to) to get:
We can conclude that the correct answer is D) 31
3. Direct substitution again, so we are going to replace in our quantity by 
to get:
And since cosine of is 0, and any quantity multiplied by zero is zero:
We can conclude that the correct answer is A) 0
4. Here we need to so some algebra first. Notice that if we use direct substitution, the denominator will be zero, and we cannot divide by zero. So lets massage our quantity first:
Now, we can use direct substitution to get:
We can conclude that the correct answer is B) 4
1. Since we are using direct substitution, the only thing we need to do is replace
We can conclude that the correct answer is B) -6
2. Again, since we are using direct substitution, th only thing we need to do is replace
We can conclude that the correct answer is D) 31
3. Direct substitution again, so we are going to replace
And since cosine of
We can conclude that the correct answer is A) 0
4. Here we need to so some algebra first. Notice that if we use direct substitution, the denominator will be zero, and we cannot divide by zero. So lets massage our quantity first:
Now, we can use direct substitution to get:
We can conclude that the correct answer is B) 4