2. Linear Functions

Question 1

General equation of a line

Answer 1

Ax + By = C

m = -A/B and b = C/B

Question 2

Slope-intercept form

Answer 2

y = mx+ b

m is slope and b is y-intercept

Question 3

Point-slope form

Answer 3

y – y₁ = m(x – x₁)

m is slope and (x_1,y₁) are the cooridinates of some point on the line

Question 4

Slope

Answer 4

m = (y₁ – y₂) / (x₁ – x₂)

(x₁,y₁) and (x₂,y₂) are the coordinates of two points

Question 5

Parallel lines…

Answer 5

have equal slopes

Question 6

Perpendicular lines…

Answer 6

have slopes that are negative reciprocals

Question 7

Distance between two points (x₁,y₁) and (x₂,y₂)

Answer 7

√( (x₁–x₂)² + (y₁–y₂)² )

Question 8

Coordinates of the midpoint between two points

Answer 8

( x₁+x₂ /2 , y₁+y₂ /2 )

Question 9

Distance between a point with coordinates (x₁,y₁) and a line Ax + By + C = 0

Answer 9

|Ax₁ + By₁ + C| / √( A² + B² )