BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.10, Problem 63E

(a)

To determine

To prove: that if x and y intercept is nonzero the equation will be of two intercept form.

Expert Solution

Answer to Problem 63E

The equation of two intercept form or xa+yb=1 .

Explanation of Solution

Given:

  xa+yb=1 .

Concept used:

During intercept of x-axis :

  y=0 .

During intercept of y-axis :

  x=0 .

Calculation:

Start from the general equation of a line:

  Ax+By+C=0 .

Find the x-intercept of the graph of this equation, set y=0 and solve for x.

  Ax+By+C=0 .

  Ax+B(0)+C=0

  Ax=-C .

The intercept of x is x=-CA .

Find the y - intercept of the graph of this equation, set x=0 and solve for y :

  Ax+By+C=0 .

  By=-C .

  y=-CB .

The intercept of y is y=-CB .

Let a the intercept so a=-CA .

Let b the intercept so b=-CB .

Back to the general equation of a line:

  Ax+By+C=0 .

  Ax+By=-C .

  A-Cx+B-Cy=1 .

  x(-CA)+y(-CB)=1 .

  xa+yb=1 .

(b)

To determine

To find:the equation using two intercept form given below.

Expert Solution

Answer to Problem 63E

Theequation is 4x-3y-24=0 .

Explanation of Solution

Given: xa+yb=1 and Set a=6 and b=-8 .

Concept used:

Two intercept form:

During intercept of x-axis :

  y=0 .

During intercept of y-axis :

  x=0 .

Calculation:

For the equation of the indicated line use the two- intercept form of linear equation:

  xa+yb=1 .

Set a=6 and b=-8 .

  x6+y8=1 .

  24x6+24y(8)-24(1)=0 .

  4x-3y-24=0 .

Hence the equation is 4x-3y-24=0 .

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