# An expression for the function whose graph is the line segment.

### 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 1.1, Problem 48E
To determine

## To find: An expression for the function whose graph is the line segment.

Expert Solution

The function of a line joining the two points (5,10) and (7,10) is f(x)=53x+53 where 5x7 .

### Explanation of Solution

Given:

The graph is the line segment joining the points (5,10) and (7,10) .

Formula used:

The slope (m) of a line segment joining the points (x1,y1)and(x2,y2) is,

m=y2y1x2x1 (1)

The equation of a line with slope (m) and a point (x1,y1) is,

yy1=m(xx1) (2)

Calculation:

Use formula (1) and obtain the slope of a line segment joining the points (5,10) and (7,10) .

Here, x1=5,y1=10,x2=7,y2=10 .

m=10(10)7(5)=2012=53

Use formula (2) and obtain the equation of line with slope m=53 and the point (−5, 10).

y10=53(x(5))=53x253

Rearrange the terms and simplify.

y=53x253+10=53x+53

Therefore the function is f(x)=53x+53 where 5x7 .

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