1. 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?

2. If line a has a greater slope than line b, is line a steeper than line b? Explain,
giving examples to support your answer.

3. 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 classmates and discuss any differences.

4. 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 y=-1/3x

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

step-by-step explanation:

consider an orange peel: if you want to try and lay it flat, you have to stretch it, we know exactly how things are being stretched or squashed at any given point. we have many different map projections because each has different patterns of some projections can even preserve certain features of the earth without