4.1 Linear Functions

Find the slope of the line that passes through the two given points. (x, y) = (4, 3) and (x, y) = (8, 11)

2/1

Terry is skiing down a steep hill. Terry's elevation E(t) in feet after t seconds is given by E(t) = 2000 − 90t. Write a complete sentence describing Terry's starting elevation and how it is changing over time.

Terry starts at an elevation of 2000 feet and descends at 90 feet per second.

Determine whether the function is increasing or decreasing. a(x) = 7 − 6x

The function is decreasing.

Determine whether the function is increasing or decreasing. j(x) = 1/3x − 7

The function is increasing.

Find the slope m of the line passing through the points (3.25, −9.19) and (3.25, 4.77). (If an answer is undefined, enter UNDEFINED.)

UNDEFINED

slope of line passing through (3.29,-9.19) & (3.29,4.72)

UNDEFINED

slope of perpendicular lines

negative reciprocals (flip and change signs) m --> -1/m

covering up method

only used with standard form

Determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular. 5y + 6x = 30 −10y = 12x + 1

parallel

Determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular. 2x − 3y = 10 3x + 2y = 1

perpendicular

If the graphs of two linear functions are perpendicular, describe the relationship between the slopes and the y-intercepts.

slope: negative reciprocals of one another. y-intercept: There is no relationship.

-4x + 7y = 56 Find x & y intercepts of equation

x = (-14,0) y = (0,8)

Find the x- and y-intercepts of the equation. −5x + 6y = 60

x-intercept: (-12,0) y-intercept: (0,10)

Find the x- and y-intercepts of the equation. f(x) = −x + 1

x-intercept: (1,0) y-intercept: (0,1)

Given the set of information, find a linear equation satisfying the conditions, if possible. (If not possible, enter IMPOSSIBLE.) passes through (x, y) = (1, 9) and (x, y) = (7, 21)

y = 2x+7

line perpendicular to y=3x-7 & passes through (3,5)

y-5 = -1/3(x-3)

Write an equation of the line in point-slope form that passes through the points (x, y) = (0, 6) and (x, y) = (3, 5). (Find the point-slope form by using (3, 5) as the primary point.)

y-5=-1/3(x-3)

point slope form

y-y1=m(x-x1)

slope formula

y2-y1/x2-x1

slope-intercept form

y=mx+b

Is 2x + y = 10 equivalent to the function f(x) = −2x + 10?

yes