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#1 2021-05-01 10:59:03

mathland
Member
Registered: 2021-03-25
Posts: 444

Using Intercept Form

Use the intercept form to find the general form of the equation of
the line with the given intercepts. The intercept form of
the equation of a line with intercepts (a, 0) and (0, b) is
(x/a)+ (y/b) = 1, where a ≠ 0, b ≠ 0.


1. x-intercept: (−3, 0), y-intercept: (0, 4)

2. Point on line: (−3, 4)
x-intercept: (d, 0), d ≠ 0
y-intercept: (0, d), d ≠ 0

I need steps for 1 and 2. I will do the math work.

Thanks

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#2 2021-05-01 11:45:27

zetafunc
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Registered: 2014-05-21
Posts: 2,432
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Re: Using Intercept Form

For #1, what are a and b in this case?

For #2, you're given a value of x and a value of y. What happens when you substitute those into the equation? Moreover, what are the values of a and b?

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#3 2021-05-02 05:27:59

mathland
Member
Registered: 2021-03-25
Posts: 444

Re: Using Intercept Form

zetafunc wrote:

For #1, what are a and b in this case?

For #2, you're given a value of x and a value of y. What happens when you substitute those into the equation? Moreover, what are the values of a and b?

1. I think a and b are constants. In that case, a = -3 and b = 4.

2. You are saying to substitute a = -3 and b = 4 into

(x/a) + (y/b) = 1

(-3/a) + (4/b) = 1

Is this what you mean?

Also, where does the x-intercept: (d, 0), d ≠ 0 and the
y-intercept: (0, d), d ≠ 0 come into play?

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#4 2021-05-02 05:34:35

zetafunc
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Registered: 2014-05-21
Posts: 2,432
Website

Re: Using Intercept Form

mathland wrote:

1. I think a and b are constants. In that case, a = -3 and b = 4.

Correct.

mathland wrote:

2. You are saying to substitute a = -3 and b = 4 into

(x/a) + (y/b) = 1

(-3/a) + (4/b) = 1

Is this what you mean?

Yes.

mathland wrote:

Also, where does the x-intercept: (d, 0), d ≠ 0 and the
y-intercept: (0, d), d ≠ 0 come into play?

What does this tell you about the values of a and b?

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#5 2021-05-02 06:33:27

mathland
Member
Registered: 2021-03-25
Posts: 444

Re: Using Intercept Form

zetafunc wrote:
mathland wrote:

1. I think a and b are constants. In that case, a = -3 and b = 4.

Correct.

mathland wrote:

2. You are saying to substitute a = -3 and b = 4 into

(x/a) + (y/b) = 1

(-3/a) + (4/b) = 1

Is this what you mean?

Yes.

mathland wrote:

Also, where does the x-intercept: (d, 0), d ≠ 0 and the
y-intercept: (0, d), d ≠ 0 come into play?

What does this tell you about the values of a and b?

The x-intercept is (d, 0) and the y-intercept is (0, d).
Given the points (a, 0) and (0, b), I say a = d and b = d.

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#6 2021-05-02 06:55:09

zetafunc
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Registered: 2014-05-21
Posts: 2,432
Website

Re: Using Intercept Form

mathland wrote:

I say a = d and b = d.

Correct.

So what's the value of d?

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#7 2021-05-03 09:02:40

mathland
Member
Registered: 2021-03-25
Posts: 444

Re: Using Intercept Form

zetafunc wrote:
mathland wrote:

I say a = d and b = d.

Correct.

So what's the value of d?

The value of d is two-fold: d = a, d = b.

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#8 2021-05-03 11:07:43

zetafunc
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Registered: 2014-05-21
Posts: 2,432
Website

Re: Using Intercept Form

You have

mathland wrote:

(-3/a) + (4/b) = 1

and

mathland wrote:

I say a = d and b = d.

How can you eliminate a and b to determine the (numerical) value of d?

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#9 2021-05-03 11:31:04

mathland
Member
Registered: 2021-03-25
Posts: 444

Re: Using Intercept Form

zetafunc wrote:

You have

mathland wrote:

(-3/a) + (4/b) = 1

and

mathland wrote:

I say a = d and b = d.

How can you eliminate a and b to determine the (numerical) value of d?

I think multiplying each term by the LCD ab will do away with a and b.

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#10 2021-05-04 20:54:28

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,432
Website

Re: Using Intercept Form

mathland wrote:

(-3/a) + (4/b) = 1

mathland wrote:

I say a = d and b = d.

What happens when you substitute a = d and b = d into the equation above?

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#11 2021-05-04 23:49:42

mathland
Member
Registered: 2021-03-25
Posts: 444

Re: Using Intercept Form

zetafunc wrote:
mathland wrote:

(-3/a) + (4/b) = 1

mathland wrote:

I say a = d and b = d.

What happens when you substitute a = d and b = d into the equation above?

Let me see.


(-3/d) + (4/d) = 1

The equation then becomes

(-3 + 4)/d = 1

When I simply the numerator, I get (1/d) = 1.

What does this mean?

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#12 2021-05-05 00:12:12

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Using Intercept Form

Therefore d = 1 and you're done.

You know already that a = b = d so you can plug into the intercept equation.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#13 2021-05-05 10:31:19

mathland
Member
Registered: 2021-03-25
Posts: 444

Re: Using Intercept Form

Bob wrote:

Therefore d = 1 and you're done.

You know already that a = b = d so you can plug into the intercept equation.

Bob

Easier than I thought.

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