Solve 2 Calculus Problems: Find Point & Write Equation

[vee123]

I have two Calculus problems I need explained because I'm studying for a final exam and I forgot how to do these things:

#1: Find the point that lies on the line determined by the points (1,-2) and (-3,1).

The answer is (5,-5), but I don't know why...


#2: Write an equation satisfied by the graph obtained by shifting y=2x-5 three units to the left.

The answer is y=2x+1

I know when an equation is shown moving to the left, it is put in parentheses and a number is added to it (for example y=x^2 becomes y=(x^2+2) when it is moved two places to the left). However, I do not know how to do this problem.

Could someone please help me?

 

[cyby]

I have two Calculus problems I need explained because I'm studying for a final exam and I forgot how to do these things:

#1: Find the point that lies on the line determined by the points (1,-2) and (-3,1).

The answer is (5,-5), but I don't know why...


#2: Write an equation satisfied by the graph obtained by shifting y=2x-5 three units to the left.

The answer is y=2x+1

I know when an equation is shown moving to the left, it is put in parentheses and a number is added to it (for example y=x^2 becomes y=(x^2+2) when it is moved two places to the left). However, I do not know how to do this problem.

Could someone please help me?

Several things you can do. First off, these aren't calc questions, afaik.

1. Can you write down the equation determined by the two points? If so, then I guess you have choices to plug into the equation to see if they work.

2. The easiest thing to do is to just plot the thing and move it 3 units to the left, and see what you get. But you can also just apply some transforms. In your case, you can shift your function to the left ( f(x) -> f(x+3) ) by applying that transform.

See what you get :)

 

[vee123]

Thanks for the reply! I think I'm starting to remember this...

Yeah I know these aren't really calc questions, but they were in the beginning section of my calc. book.

Thanks for your help!

 

[cyby]

Anytime :D

 

[vee123]

Okay, I'm still having trouble with the second question. I know I may sound really stupid, but I tried to solve it by doing f(x)=(2x-5+3), and did not get the correct answer. What am I doing incorrectly?

 

[cyby]

Consider rewriting f(x) = 2x-5 as f(x) = 2(x-5/2).. and see if you get anything from there...

 

[vee123]

Now I understand! I was having a bit of a mental block at hte moment... Thank you very much! :)