Calculus - P.2 Linear Models and Rates of Change

Question 0

Possibilities for slope of a line

Answer 0

1. m>0 -> rises to the right
2. m<0 -> rises to the left
3. m is undefined -> n/0 -> vertical
4. m=0 -> horizontal

Question 1

Slope

Answer 1

Rate of change, rise/run, steepness, slant, tilt

Formula:
y2-y1/x2-X1

Note 1: Any two collinear points will have the same slope

Note 2: Ratio: Dy/Dx

Question 2

Point-Slope Form

Answer 2

y=m(x-X1)+y1

Used: When a slope and a point are given

Question 3

Slope-Intercept Form

Answer 3

y=mx+b

Used: Almost always whenever an “equation” of a line is asked for

Question 4

General Form

Answer 4

Ax+By+C=0

Must have: A-B-C order, no fractions, Ax_>0
Used: Sparingly => only when asked

Question 5

Vertical line

Answer 5

X=c,
where c is the x-coordinate of the points

Used: When slope is undefined

Question 6

Horizontal line

Answer 6

Y=b,
where b is the y-coordinate

Used: When the slope is 0

Question 7

Perpendicular lines

Answer 7

Slopes are negative reciprocals

m1=1/m2 flip and change sign

Question 8

Parallel lines

Answer 8

m1=m2

Slopes are the same