24 years since ALGEBRA...a little help please...3 questions?

Question

I'm flying along...answered over 200 of these correct...BUT..when I get stumped...I'm really stumped... can you help me w/ these. I got wrong answers and don't know WHY.. thanks!!!

write the slope intercept form of the line and then identity slope and y intercept

1/3x - 2/5y =1

Use slope-point formula if possible to write equation of the line given the following information. Write final answer in slope intercept form if possible.

Slope is 4.1 and the line passes through the point (5.3, -2.2)

next w/ same instructions:

The line passes through the points (1, -3) and (-7, 2)

Thank you so much. I can't wait to "see" where I made my wrong turn... these have drove my rusty math braincells crazy.. LOL

Answer 1

If you know hoew to do 200 of these correct, then you dont have to ask!

You dont put the questions numbers either, so i think you are not pay attention in class, or you do not organize your work well.

For number 1) you shold not write 1/3x - 2/5y = 1, it should be

(1/3)x - (2/5)y = 1.

I will do the first one for you, the rests, you will need to work for another "200 of these" questions again.

1) (1/3)x - (2/5)y = 1

(2/5)y = (1/3)x - 1            (move (2/5)y, and move 1)

y = (5/2)*(1/3)x - (5/2)*1

y = (5/6)x - (5/2) is the answer.

The slope = 5/6 the y-int = - (5/2)

Good Luck!

Answer 2

1/3x - 2/5y = 1

-2/5y = 1 - 1/3x

y = (1 / -2/5) - (1/3x / -2/5)

y = 5/-2 + 5/6x

=====================

(y + 2.2) / (x - 5.3) = 4.1

4.1(x - 5.3) = y + 2.2

4.1x - 21.73 = y + 2.2

y = 4.1x - 23.93

=====================

SLOPE = (2 + 3) / (-7 - 1)

SLOPE = 5/-8 = -5/8

Using the slope formula again:

(y - 2) / (x + 7) = -5 / 8

Cross mutiply:

8(y - 2) = -5(x + 7)

8y - 16 = -5x - 35

8y = -5x - 19

y = -5/8x - 19/8

Answer 3

I expect the first one means

(1/3)x - (2/5)y = 1 (a bit difficult writing fractions all on one line)

We want to get y on its own on one side.  Shift it to the right and take 1 to the left:

(1/3)x - 1 = (2/5)y

Multiply both sides (each term) by 5

(5/3)x - 5 = 2y

Divide both sides by 2

(5/6)x - 5/2 = y

We could have done those last two steps in one hit, just multiply both sides by 5/2.

Anyway, result is as you see, and so

slope = 5/6 and y intercept is -5/2 (i.e. -2.5)

With slope 4.1, equation is

y = 4.1x + b

Passes thru (5.3, -2.2) therefore

-2.2 = 4.1*5.3 + b

b = -2.2 - 4.1*5.3

.. = -23.93

Hence equation is y = 4.1x - 23.93

Given two points, calculate gradient

(2 -(-3))/(-7 -1)

= -5/8

Equation is

y = (-5/8)x + b

Thru (1, -3):

-3 = -5/8 + b

b = -3 + 5/8

.. = - 19/8

Equation is

y = (-5/8)x - 19/8

Once we have the gradient, these can also be done by using the formula

y-y1 = m(x - x1)

y - (-3) = (-5/8)(x - 1)

y + 3 = (-5/8)x + 5/8 as before.

When there are fractions in it, I'm tempted to put it in the other form:

Multiply by 8:

5x + 8y + 19 = 0

Notice both the given points satisfy this equation.