Chapter 4 Flashcards
How do you properly graph linear equations?
1) Make a table of values
2) Plot ordered pairs
3) Draw a line through the points
4) Make sure line is accurate (corner to corner, arrows on the ends)
5) Write equation on graph
The graph of x=a is a horizontal line passing through _______.
the y axis
(0,b)
The graph of x=a is a vertical line passing through ______.
The x axis
(a,0)
Make a table for the equation y = 1/2x - 1
x y
0 -1
2 0
4 1
Plug the numbers in the x column into the equation
Find the slope of the line through the points (3,7) and (5,19)
m= 19-7/5-3 = m= 12/2
m=6
Is a zero line horizontal or vertical?
Horizontal
Is a undefined line horizontal or vertical?
Vertical
Is the top of a positive line in quadrant I or II?
Quadrant I
Is the top of a negative line in quadrant I or II?
Quadrant II
x y
1 2
3 10
5 18
7 26
Find the slope.
m = 4
(r,3) (5,9)
m = 2
Find the value of r
r = 2
Non Vertical parallel lines have the ______ _______.
Same slope.
The graph of _______ is a line with a slope of m that passes through the ______.
y=mx+b
origin
On a graph, direct variation must be a ________ ____ and go through the _____.
Straight line
Origin
In y = mx + b, b equals?
The initial value
y intercept
In y = mx + b, m equals?
The rate of change, or slope
Suppose y directly varies with x.
If y is 20 when x = 4, find y when x = 3
y = 15
Suppose y varies with x.
If y is 2 when x=8, find x when y equals 9.
x = 36
y = -7x + 9
Find the slope and y intercept.
Slope: -7/1
Y intercept: 9
y = x - 12
Find the slope and y intercept.
Slope: 1/1
Y intercept: -12
y + 8 = -3x
Find the slope and y intercept.
Slope: -3/1
Y intercept: -8
2y + 10 = 4x
Find the slope and y intercept.
Slope: 2/1
Y intercept: -5
The height (y) of a moveable bridge after rising for x seconds is represented by the equation y = 3x+ 16. Interpret the y intercept and slope.
How many seconds does it take for the bridge to reach a height of 76 feet?
x = 20
The bridge has a height of 16 feet and rises 3 feet per second.
It would take 20 seconds for the bridge to reach a height of 76 feet.
The cost (y) in dollars for making x friendship bracelets is represented by the equation y = 0.5x + 2. Interpret the y intercept and slope.
The bracelets cost 2 dollars plus 50 cents per bracelet
The number of perfume bottles in storage after x months is represented by the equation y = -20 + 460. Interpret the y intercept and slope.
In how many months will there be no perfume bottles left in storage.
There were 460 bottles, and 20 bottles get taken out per month.
It will take 23 months for there to be no more bottles in storage.
5x + y = -5
Find the X and Y intercepts.
x intercept = -1
y intercept = -5
2x + 9y = 18
Find the X and Y intercepts.
x intercept = 9
y intercept = 2
1.5x + 0.6y = 6
Find the X and Y intercepts.
x intercept = 4
y intercept = 10
1.2x + 0.8y = 12
Find the X and Y intercepts.
x intercept = 10
y intercept = 15
Students tickets cost 9 dollars and general tickets cost 15 dollars. On one day they collected 4500 dollars. If X represents student tickets and y represents general tickets, find the x and y intercepts.
Interpret the x and y intercepts.
9x + 15y = 4500
x intercept = 500
y intercept = 300
You could buy 500 student tickets and 0 general tickets.
You could buy 300 general tickets and 0 student tickets.
Is 5x + y = -5 in slope intercept form?
No, standard form
