# To show that the equation of line can be put in the form x a + y b = 1

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter B, Problem 46E

(a)

To determine

## To calculate: To show that the equation of line can be put in the form xa+yb=1

Expert Solution

It is proved thatequation of line can be put in the form xa+yb=1

### Explanation of Solution

Given information: a and b are x-intercepts and y-intercepts respectively

Formula Used:

Slope of the line passing through the points P1(x1,y1) to P2(x2,y2) is

m=y2y1x2x1

Equation of line having slope m and passing through the point P1(x1,y1) is

yy1=m(xx1)

Calculation:

Given that a and b are x-intercepts and y-intercepts respectively

Thus, points are as follows:

(a,0) and (0,b)

Slope of line passing through above two points is calculated as

m=0ba0m=ba

Now, equation of line passing through (a,0) is calculated as

y0=ba(xa)y=bax+byb=1ax+1yb=xa+1xa+yb=1

Conclusion:

Hence, proved that equation of line can be put in the form xa+yb=1

(b)

To determine

### To calculate: To find the equation of line

Expert Solution

The equation of line is x6y8=1

### Explanation of Solution

Given information: x-intercept is 6 and y-intercept is 8

Formula Used:

If a and b are x-intercept and y-intercept respectively, then equation of line can be put in the form xa+yb=1

Calculation:

Given x-intercept is 6 and y-intercept is 8

Thus,

a=6b=8

Equation of line in two-intercept form is given as

xa+yb=1

Substituting the values,

x6+y8=1x6y8=1

Conclusion:

Hence, the equation of line is x6y8=1

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