# An expression for the function whose graph is the line segment joining the points ( 1 , − 3 ) and ( 5 , 7 ) . ### 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 47E
To determine

## To find: An expression for the function whose graph is the line segment joining the points (1,−3) and (5,7).

Expert Solution

The function of a line joining the points (1,3) and (5,7) is f(x)=52x112 where 1x5_.

### Explanation of Solution

Given:

The graph is the line segment joining the points (1,3) and (5,7).

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 (1,3) and (5,7).

Here, x1=1,y1=3,x2=5,y2=7.

m=7(3)51=7+34=104=52

Use formula (2) and obtain the equation of a line with slope m=52 and the point (1,3).

y(3)=52(x1)y+3=52x52y=52x523y=52x112

Therefore the function is f(x)=52x112 where 1x5.

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