2-13-24 Linear Equation Notes

P4 A. Which lines shown have positive slope? Which

have negative slope?

Groups:

(a) Positive Slope

,

(b) Negative Slope

• Line 1

• Line 3

• Line 4

• Line 2

P4 B-C. Of the two lines with positive slope, ​ (a)   rises more steeply.

Of the two lines with negative slope, ​ (b)   falls more steeply.

• Line 3
• Line 2
• Line 4
• Line 1

P4 D. Line 4 has a slope of 1/2. Line 1 has a slope of -1. Of these two lines, which is steeper? How can you tell from the given slopes?

|-1| _ |1/2|

Mathematical Equivalence

ON

P4 E. For the blue line, why is the rise a negative number?

As the ​ (a)   ​ (b)   from the first point to the second point, the ​ (c)   ​ (d)   .

• x-values
• y-values
• increase
• decrease

P5 A. The rise = ​ (a)   . The rise represents a ​ (b)   in the amount of ​ (c)   remaining. The units are in ​ (d)   .

• -7
• decrease
• gasoline
• gallons
• 7
• increase
• distance traveled
• miles

P5 B. The run = ​ (a)   . The run represents an ​ (b)   in the ​ (c)   . The units are ​ (d)   .

• 210
• increase
• distance traveled
• miles
• -210
• decrease
• gasoline left
• gallons

P5 C. The slope = ​ (a)   . The slope represents a ​ (b)   by ​ (c)   for every (d)   . The units are ​ (e)   .

• -1/30
• 1 gallon of gasoline
• gallons per mile
• 30 miles traveled
• decrease
• -30/1
• increase
• miles per gallon
• 1/30
• -7/210

P6 3A. ​ (a)   ; If (4, 5) is designated as ​ (b)   and (-3, -6) is designated as ​ (c)   , both subtractions would be done in the ​ (d)   order and the result would be ​ (e)   .

• Yes
• opposite
• 11/7
• No
• same
• -11/7

P6 3B. ​ (a)   . The slope formula is ​ (b)   . If the ​ (c)   ​ (d)   done in the same order, the result will be the ​ (e)   the correct slope.

• Yes
• subtractions
• are not
• opposite of
• No
• additions
• are
• same as

P6 4A. The slope is a ​ (a)   fraction, so thinking of both the numerator and denominator as ​ (b)   values means that the rise and run are both in the ​ (c)   direction. For the rise, this is ​ (d)   ; for the run, this is to the ​ (e)   .

• positive
• up
• right
• negative
• down
• left
• large
• small