# To prove: that if x and y intercept is nonzero the equation will be of two intercept form. ### Precalculus: Mathematics for Calcu...

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

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

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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