Show:
Graphing Linear Functions
Slope and Rate of Change
Slope-Intercept Form
Direct Variation
Function Notation
100
Given point (-4, 3), this is the quadrant the point lies in.
What is quadrant II.
100
This is the formula for finding slope given 2 points (x1, y1) and (x2, y2).
What is m = (y2 - y1)/(x2 - x1)
100
Given the linear equation y = mx + b, this letter represents slope and this letter represents y-intercept.
What is slope = m and y-intercept = b
100
Given y = x, this is the constant of variation of the function.
What is 1.
100
Given f(x) = x + 1, this is f(3).
What is 4
200
Given point (0, 6), this is the quadrant the point lies in.
What is no quadrant, since the point is on the y-axis.
200
This is the slope of the line that passes through points (-1, 11) and (2, 10).
What is m = -(1/3)
200
This is the slope and y-intercept for equation y = 2x + 3
What is m = 2 and b = 3
200
Given y varies directly with x, this is the direct variation equation and constant of variation if x = 5 and y = 10.
What is y = 2x and 2
200
Given g(x) = 6x - 5, this is g(4).
What is 19
300
This is the x- and y-intercepts of the linear equation 2x - 6y = 6
What is x-intercept (3, 0) and y-intercept (0, -1).
300
This is the slope of the line that passes through points (-2, 5) and (4, 5).
What is m = 0
300
This is the slope and y-intercept of 4x + 2y = 10
What is m = -2 and b = 5
300
Given y varies directly with x, this is the direct variation equation and constant of variation if x = 4 and y = 6.
What is y = (3/2)x and 3/2
300
Given f(x) = 3x + 3, this is the input value that makes f(x) = 12
What is x = 3
400
Given function -2x + y = 2 with domain D = {x | x >= 0}, this is the range of the function. (hint: graph it!)
What is R = {y | y >= 2}
400
This is the slope of the line that passes through points (5, -6) and (5, 10).
What is m is undefined.
400
This is the slope and y-intercept of -3x + 4y - 12 = 0.
What is m = (3/4) and b = 3
400
This answers whether y = 5x + 7 is a direct variation and why or why not.
What is no, it does not go through the origin (the y-intercept is not 0)
400
Given h(x) = 10x + 3, this is the input value that gives an h(x) value of 23.
What is x = 2
500
This verbally describes the graph of the function y = -10
What is a horizontal line with y-intercept (0, -10) (or a horizontal line that passes through point (0, -10).
500
Suppose a graph shows the altitude of a plane during 3 hours of flying: between hours 0 and 1 the plane went from 0 feet to 30,000 feet; between hours 1 and 2 the plane went from 30,000 to 35,000, and between hours 2 and 3 it went from 35,000 to 0 feet. This gives us a) the rate of change between the intervals as well as b) the time interval that saw the greatest rate of change. (hint: graph this first!).
What is a) 30,000, 5,000, -35,000 and b) the interval between hours 2 and 3.
500
This explains how to graph 2x + y = -1 using the slope-intercept method
What is find the slope (m = -2) and y-intercept (b = -1), plot the y-intercept, and then from the y-intercept go down 2 and to the right 1 to find other points, which are then connected.
500
Given that the pay you make varies directly with the number of hours you work, and you made $84 when you worked 12 hours, this is the direct variation equation for the situation, as well as the pay if you work 16 hours.
What is p = 7h and $112
500
Given f(x) = x and g(x) = x + 5, this explains the transformation that takes place between the two functions.
What is g is f translated up 5 units.