Unit 6 & 7: Linear Relations and Linear Equations

Diagonal/Oblique lines

constant change over time

Horizontal lines

no change has occurred

Curved lines

change is not consistent

Continuous

the variable can by any number

Discrete

the variable can only be certain values

Interval notation

square brackets (point is included)

round brackets (point not included)

infinity always have a round bracket

domain

all the defined x values for a relation

range

all the defined y-values for a relation

function

a relation that has exactly 1 y-coordinate for each x-coordinate. All functions pass the vertical line test

what does positive slope mean?

line is increasing

what does a negative slope mean?

line is decreasing

x-intercept

where the relation crosses the x axis, y = 0

y-intercept

where the relation crosses the y axis, x = 0

slope (m)

describes the rate of change of a LINEAR function

in general form the a and b must be what?

• positive, whole number

• integer

• no fractions for a and b

• a and b aren’t both 0

parallel lines

lines that have different intercepts but identical slopes and are always equal distance apart

perpendicular lines

intersect at a 90 degree angle. Their slopes are NEGATIVE RECIPROCALS of each other. The product of these slopes is -1

what does compare these lines mean?

compare means to state what is the same and what is different

Vertical line test

draw a vertical line down the graph, the line should only touch one point on the graph

What is the slope of a horizontal line?

0

What is the slope of a vertical line?

undefined

Collinear

points on the same line (the ordered pairs slopes should be the same