Algebra 1
Algebra 1
1st Edition
ISBN: 9780078884801
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Concept explainers

Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …
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Chapter 3.3, Problem 51HP
To determine

To explain how the rate of change and slope are related and how to find the slope of a line.

Expert Solution & Answer
Check Mark

Explanation of Solution

Concept Used:

Equation of the line passing through the points (x1,y1) and (x2,y2) is given by y−y1=m(x−x1) , where slope, m=y2−y1x2−x1 .

Calculation:

The slope of any line is given by rise over run. That is, the ratio of the number of units it rise or fall over the number of units it move forward or backward from a fixed point.

The rate of change is a ratio to describe how much one quantity is changing with respect to a change in another quantity.

The slope of the line is the instantaneous rate of change at any point.

The slope of a line can be found using rise over run method. In this method, start from any point on the line and then find the ratio of the count the units moved up/down to the count of units moved forward/backward. If the units measured for going upward or forward then take the units with positive sign. And if the units measured are in downward or backward direction, then take the number of units with negative sign.

For example, the slope of the line passing through the points (a,b) and (c,d) is given by

  slope, m=y2−y1x2−x1m=d−bc−a

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Chapter 3.3, Problem 50HP
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Chapter 3 Solutions

Algebra 1

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