   Chapter 10.2, Problem 45E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Where m < 0 and b > 0 , the graph of y = m x + b (along with the x and y axes) determines a triangular region in Quadrant I. Find an expression for the area of the triangle in terms of m and b .

To determine

To find:

An expression for the area of the triangle in terms of m and b which is formed by the graph of y=mx+b (along with the x and y axes) in Quadrant I in which m<0 and b>0.

Explanation

Consider the line equation y=mx+b.

The graph of this line equation by considering m<0 and b>0.

The general formula for the area of the triangle is 12(base×height).

The x-intercept and y-intercept can be found by

Substitute x=0 in the equation y=mx+b.

y=m0+b

y=b

The point is 0, b.

Substitute y=0 in the equation y=mx+b.

0=mx+b

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