Linear Functions

Do Now: How do we know if a set of data represents a linear function?

Check the rate of change (slope) and see if it is constant

Do the following represent linear functions?

x 2 3 5 8 10

y 5 9 17 29 37

t 0 1 4 5 8

h 3 5 10 11 17

How do we write the equation of a line?

1. Use slope/intercept (y = mx + b) if given slope and y-intercept

2. Use point/slope (y - y1 = m(x - x1))if given point and slope or 2 points (find slope)

Find an equation of a line for each of the following:

1. Slope = 6, y-intercept = 4

2. Slope = - 3, passing through (- 1, 4)

3. Passes through (-2,1) and (1,-5)

4. f(-1) = 4 and f (1) = 0

Complete each of the following:

Parallel lines have ______________ slopes

Perpendicular lines have ________________ slopes

Vertical lines have ______________ slopes

Horizontal lines have _________________ slopes

A linear function is increasing when the slope is _____

A linear function is decreasing when the slope is _____

How do we find the equation of the perpendicular bisector?

Ex. Find the equation of the perpendicular bisector of the segment joining (-1,2) and (3,6)

1. Find the slope of the line segment - use negative reciprocal

2. Find the midpoint of the line segment

3. Write the equation using the midpoint and the negative reciprocal slope.