Intro Calculus (grade/year 11) question. Equations in form: y=mx+c...?

Question

Express each of the following equations in the form y=mx+c

a) 3x-2y=12
b). 4y-5=2x+5
c). 3(x-1)=4(y+2)
d). x/3+y/6=1

Question 2:
Find the gradient, x-intercept and y-intercept of the line

x/a+y/b=1 where a and b are constants

Question 3: Solve the following simultaneous equations algebraically:

3x-2y=12 and 2x-5y=19

Question 4: Factorise the following functions completely:

a). f(x)=x^2-3x-10
b). g(x)=2x^2-7x+3
c). h(x)=3x^2-7x-6

Thankyou. Please clearly show all of the working out and which question and answer each one is (question 1, 2, 3 or 4 and a b or c of each).
Thanks.

Sorry I didn't mention..I found it all easy...I just want to make sure I got all the questions and the layout correct. Please help!

I promise I am just checking my answers..honestly! It's not homework anyway.

Answer 1

are you trying to get strangers to do your homework?

the first questions are all just a matter of basic algebra.
1a) 3x-2y=12
subtract 3x from both sides:
-2y=12-3x
divide by -2
y=-6+(3/2)x
re-arrange
y=(3/2)x-6
voila! m=(3/2) b=6

you can do parts b,c,d on your own unless someone else answers them for you.

Question 2:
the y intercept is where x=0
0/a+y/b=1
y/b=1
multiply by b
y=b

the x intercept is where y=0
same thing:
x/a+0/b=1
x/a=1
multiply by a
x=a

for the gradient (slope) we need to get into y=mx+b form
again just algebra
x/a+y/b=1
subtract x/a
y/b=1-x/a
multiply by b
y=b-(b/a)x
gradient=b/a

Question 3:
solve algebraically,
3x-2y=12
2x-5y=19
there's a number of ways to do this, I'm not sure which you are familiar with. My personal favorite is cancellation

multiply the first equation by 2 and the second by three to get
6x-4y=24
6x-15y=57
now subtract the two equations:
0x+11y=-33
divide by 11
y=-3
now substitute y=-3 back into one of the equations
3x-2(-3)=12
3x+6=12
subtract 6
3x=6
divide 3
x=2
the solution is x=2, y=-3

Question 4
I'm going to be naughty and not explain myself on these it's late and I'm tired
a)(x+5)(x-2)
b)(2x-1)(x-3)
c)(3x+2)(x-3)

ta daa!

Answer 2

Look familiar?
Introductory calculus (grade/year 11) question...?
Express the following equations in the form y=mx+c

1. 3x-2y=12
2. 3(x-1)=4(y+2)
3.x/2+y/6=1
(number 3 of the question, they are both fractions on the left hand side of the equals sign that is x is the numerator and 2 is the denominator etc)

Question 2:
Solve the following simultaneous equations algebraically:

1. 3x-2y=12
2. 2x-5y=19

Thankyou for your help. Please clearly write what each answer is for (question 1 or 2 and what number the answer is (1, 2 or 3 of question 1 etc). Thankyou

Answer 3

Your answer is spot on: 3y + x = 3 Subtract x from the two components 3y = -x + 3 Divide the two components by 3 y = -x/3 + 3/3 y = (-a million/3) x + a million it incredibly is a line with slope (-a million/3) and y intercept of (0,a million)

Answer 4

I'm sorry to say this but if you can't even do review problems that prepare you for calculus, you will be VERY lost during the remainder of the class. First question is just a review of slope intercept formula... Second question is just a review of ellipse equation.... Third question is review of system of equations... Fourth question is simple factoring...