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#1 2021-05-01 10:59:03
- mathland
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- 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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#3 2021-05-02 05:27:59
- mathland
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- Registered: 2021-03-25
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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?
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
Re: Using Intercept Form
1. I think a and b are constants. In that case, a = -3 and b = 4.
Correct.
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.
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
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- Registered: 2021-03-25
- Posts: 444
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?
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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#7 2021-05-03 09:02:40
- mathland
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- Registered: 2021-03-25
- Posts: 444
Re: Using Intercept Form
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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#9 2021-05-03 11:31:04
- mathland
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- Registered: 2021-03-25
- Posts: 444
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?
I think multiplying each term by the LCD ab will do away with a and b.
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#11 2021-05-04 23:49:42
- mathland
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- Registered: 2021-03-25
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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?
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
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- Registered: 2010-06-20
- Posts: 10,640
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 
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#13 2021-05-05 10:31:19
- mathland
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- Registered: 2021-03-25
- Posts: 444
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
Easier than I thought.
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