The phrase miles per hour is an example of a rate of change. what other rates of change commonly used in everyday speech can you think of? if line a has a greater slope than line b, is line a steeper than line b? explain, giving examples to support your answer. which form of a linear equation do you prefer to use: slope-intercept form or point-slope form? list advantages and disadvantages of each. compare your answer with a classmate's and discuss any differences. there is a geometric theorem that says "if two lines in a plane are perpendicular to the same line, they are parallel to each other." explain why this is true by writing and comparing equations for two different lines that are perpendicular to .

I can answer 3 of these for you

1. Another common phrase is during cooking. I.E. 3 eggs per pancake or 6 eggs per 2 pancakes

2. Yes it would, the greater the slope the steeper it goes, so if line A is has a bigger slope than line B its steeper

3.slope intercept is good for graphing, but not for finding the point of intersection.

point slope is decent for finding the slope, but it SUCKS for graphing.

your decision on what is best

(1) "km per hour" and "price per person"

(2) Yes, line a steeper than line b because steeper line has greater slope.

(3) I prefer point-slope form.

(4) Slope of two parallel is same.

Step-by-step explanation:

(1)

The phrase "miles per hour" is an example of a rate of change.

The rates of change "km per hour" and "price per person" are commonly used in everyday speech.

(2)

If the slope of first line is greater than the slope of second line, then first line is steeper then the second line.

It is given that line a has a greater slope than line b.

Therefore the line a steeper than line b.

For example: Line a: and Line b: , then the line a is steeper than b.

(3)

Slope intercept form:

where, m is slope and b is y-intercept.

Advantages: Slope and y-intercept can easily obtained.

Disadvantages: Vertical line can not be defined in this form.

If a line passes through a points with slope m, then the point slope form of the line is

Advantages: Slope and a point can easily obtained.

Disadvantages: It is not a simplified form. It can not be written in function form.

I prefer slope-intercept form.

(4)

"If two lines in a plane are perpendicular to the same line, they are parallel to each other."

The given equation is

The slope of this line is -1/3.

The product of slops of two perpendicular lines is -1 and the slope of two parallel lines are same.

So, the slope perpendicular lines is 3.

The equations of two lines which are perpendicular to given line are

                (1)

                (2)

The slope of these lines is 3.

Since both lines (1) and (2) have same slope, therefore they are parallel.

Hence proved.

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step-by-step explanation:

yes

step-by-step explanation: