Linear equation, point slope conversion

[amerikantech]

Homework Statement

convert:
Y − 200 = −4 (X − 15)
to
X = −0.25 ⋅ Y + 65.

with a given Δy/Δx = -36/4

Homework Equations

point slope, slope intercept

The Attempt at a Solution

I understand point slope, slope intercept, and standard form, I understand how to convert one to the other, but I do not understand this conversion. I understand that .25 is the reciprocal of 4, but where does the 65 come from on the bottom equation for the y intercept? I found that if you convert the top equation to slope intercept form (y= -4x+260) and plug 0 into y then x will equal 65.

 

[lekh2003]

Ok, let me try to help you.

I understand that .25 is the reciprocal of 4

Just think of this as 1/4, no need to complicate it.

I understand point slope, slope intercept, and standard form, I understand how to convert one to the other, but I do not understand this conversion.

Don't think of the conversion as a set step of moves you need to execute to convert. You are trying to reach a goal. In this case, you are trying to move an equation of form $y-a=m(x-b)$ to an equation with one variable on one side and everything else on the other side.

Think about what algebra will be involved in the question, don't think about conversions. What operations? What techniques?

Write down each step carefully and think about what you are doing each step of the way.

 

[BvU]

Hi tech,

You rewrote to y = f(x) but the exercise wants x = g(y), so bring -4x to the left (add 4x on both sides), and y and the constants to the right .

with a given Δy/Δx = -36/4

what do those words have to do with the exercise ?

 

[Chestermiller]

What do you get if you solve for x in terms of y?

 

[scottdave]

...with a given Δy/Δx = -36/4

The Attempt at a Solution

...but where does the 65 come from on the bottom equation for the y intercept? I found that if you convert the top equation to slope intercept form (y= -4x+260) and plug 0 into y then x will equal 65.

I don't think the Δy/Δx = -36/4 belongs with this problem. The equation is for a straight line, therefore has a constant slope (Δy/Δx), and it is not equal to -36/4.

As far as the 65. When you have an equation y = some function, the constant portion of that function will be the y-intercept.

So if you have x = some function, the constant portion of that function will be the x-intercept.

 

[amerikantech]

Ok, let me try to help you.

Just think of this as 1/4, no need to complicate it.

Don't think of the conversion as a set step of moves you need to execute to convert. You are trying to reach a goal. In this case, you are trying to move an equation of form $y-a=m(x-b)$ to an equation with one variable on one side and everything else on the other side.

Think about what algebra will be involved in the question, don't think about conversions. What operations? What techniques?

Write down each step carefully and think about what you are doing each step of the way.

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You are right, this problem I thought about too much I found out 4x/4 = 1/4 * y + 260/4, thank you

 

[Chestermiller]

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You are right, this problem I thought about too much I found out 4x/4 = 1/4 * y + 260/4, thank you

I think you’re missing a minus sign.

 

[amerikantech]

correction the slope was -36/9 and I justed added the slope for extra information. I meant to put the coordinate (15,200) for added information as well.

Thank you all for the replys, I found that I was thinking about the problem a little too much. This problem came from a given example that I was trying to understand.

what the problem was doing: Y − 200 = −4(X − 15) => 4x/4 = -1/4 * y + 260/4 => X = −0.25 * Y + 65

 

[amerikantech]

I think you’re missing a minus sign.

yes, thank you, I do that way too often

 

[Mark44]

with a given Δy/Δx = -36/4

correction the slope was -36/9

Why are you writing these numbers in these unsimplified forms? -36/4 = -9 (which has nothing to do with this problem), and -36/9 = -4. You're making things harder for yourself by not simplying fractions.

 

[amerikantech]

Why are you writing these numbers in these unsimplified forms? -36/4 = -9 (which has nothing to do with this problem), and -36/9 = -4. You're making things harder for yourself by not simplying fractions.

It was just added info to explain where my slope came from in case someone asked, so I just threw whatever I had out there. I initially made the error puting the simplified form in the denominatior and thought I had acknowledged that, sorry. Next time I will only include what I am after.

 

[scottdave]

So how did you get from a slope of -9 to y = -4x plus something? That equation is saying slope of -4, not -9. Did you mean to say -36/9 perhaps?

 

[amerikantech]

So how did you get from a slope of -9 to y = -4x plus something? That equation is saying slope of -4, not -9. Did you mean to say -36/9 perhaps?

yes, I initially made the error puting the simplified form in the denominatior. -36/9 was supposed to be the original slope