4.1
Is the linear equation 3x - 2 = y in standard form? Explain.
No; it is not in the form A+By=C
The ______ is the y-coordinate of the point where a graph crosses the y-axis. (x-intercept or y-intercept)
y-intercept
In the equation y = mx + b, the value of m is the ______, and the value of b is the _____.
slope; y-intercept
Find the slope of the line.
5y= 160+ 9x
9/5
Tell whether each equation represents a direct variation. If so, identify the constant of variation.
y = 4x + 9
No
Tell whether the given ordered pairs satisfy a linear function.
{(1, 7) , (3, 6) , (6, 5) , (9, 4) , (13, 3)}
No; a constant change of -1 in y corresponds to different changes in x.
Find the x- and y-intercepts.
-2y + x = 2y - 8
x-int.: -8; y-int.: 2
The slope of any nonvertical line is ______? . (positive or constant)
constant
Find the slope that contains each pair of points.
(-9,-5) and (6,-5)
0
Tell whether each relationship is a direct variation.
x: 6 9 17
y: 13.2 19.8 37.4
Yes
Helene is selling cupcakes for $0.50 each. The function f (x) = 0.5x gives the total amount of money Helene makes after selling x cupcakes.Give its domain and range.
D: whole numbers;
R: nonneg. multiples of 0.5
Find the x- and y-intercepts of 2x + 5y = 10.
The x-intercept is 5. The y-intercept is 2.
A ladder is leaned against a building. The bottom of the ladder is 9 feet from the building. The top of the ladder is 16 feet above the ground. What is the slope of the ladder?
16/9
Find the rate of change for the number of cricket chirps per minute changes with the air temperature.
Temperature(oF)- 40 50 60 70 80 90
Chirps per minute- 0 40 80 120 160 200
4 chirps per 1oF
The value of y varies directly with x, and y = 1/2 when x = 3. Find y when x = 1.
1/6
Each equation below is linear. Write each equation in standard form and give the values of A, B, and C.
4y=7x
7x - 4y = 0; A = 7, B = -4, C =0
What is the y-intercept of 60x + 55y = 660?
12
The Lookout Mountain Incline Railway in Chattanooga, Tennessee, is the steepest passenger railway in the world. A section of the railway has a slope of about 0.73. In this section, a vertical change of 1 unit corresponds to a horizontal change of what length? Round your answer to the nearest hundredth.
1.37
A line with slope -1/3 could pass through which of the following pairs of points?
(0,-1/3) and (1,1)
(0,0) and (-1/3,-1/3)
(-6,5) and (-3,4)
(5,-6) and (4,3)
(-6,5) and (-3,4)
Tell whether each relationship is a direct variation.
-15x+4y=0
Yes; written as y=15/4x
One inch is equal to approximately 2.5 centimeters. Let x represent inches and y represent centimeters. Write an equation in standard form relating x and y. Give the values of A, B, and C.
2.5x- y = 0; A = 2.5, B = -1, C = 0
A bamboo plant is growing 1 foot per day. When you first measure it, it is 4 feet tall. Write an equation to describe the height y, in feet, of the bamboo plant x days after you measure it. What is the meaning of the y-intercept in this problem?
y=x+4; original height of the bamboo plant
The table shows a person’s heart rate over time. Show the rates of change.
change.
Time (min): 0 2 5 7 10
Heart Rate (beats/min): 64 92 146 84 64
14, 18, -31, -20/3
Find the slope of the line described by each equation.
7x + 13y = 91
-7/13
Tell whether each relationship is a direct variation. If so, identify the constant of variation.
x: -6 -2 0 3
y: -3 -1 0 1.5
Yes; 0.5