A linear function that represents the number of animals adopted from the shelter is compared to a different linear function that represents the hours volunteers work at the shelter each week. Describe the key features of the functions that are needed to determine if these lines intersect.

Step-by-step explanation:

point slope form

y-y1=m(x-x1)

slope-intercept form

y=mx+b

slope formula

y2-y1/x2-x1

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

UNDEFINED

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

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

slope of perpendicular lines

negative reciprocals (flip and change signs)

m --> -1/m

covering up method

only used with standard form

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

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

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.

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.

e) none of the above because the measure of angle cba is 101°

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.