Write the ordered pairs that correspond to the points labels A, B, C and D in the coordinate plane. (see attachment)
A (1, 2)
B (4, -1)
C (0, 3)
D (-3.-2)
100
Rewrite the equation in slope-intercept form, then find the slope and y-intercept.
y = 3(x+2)
Slope-intercept form: y=3x+6
m=3
b=6
100
Draw a graph of an increasing linear equation. Draw a graph of a decreasing linear equation.
Increasing: Line should go UP from left to right.
Decreasing: Line should do DOWN from left to right.
100
Find the slope of the graph of the line.
(See attachment)
slope = rise/run
slope = 2/1 = 2
100
What is the definition of a function.
A relation is a function if and only if for each input, there is exactly one output.
200
Plot and label the ordered pairs in a coordinate plane.
(5, 5) (-3, 4) (2, -4) (3, 0)
See individual answers.
200
Decide whether the two points lie on the graph of the line. (Are the points a solution to the equation?)
y = -3x + 1
A. (0, 1) B. (-1, 4)
y = -3x + 1
A. (0, 1)
Solution:
1 = -3(1) + 1
1 = -2 Not a solution
4 = -3(-1) + 1
4 = 4 Solution
200
Find the x and y-intercept of the equation.
x - y = 5
Solution:
x-int(plug in zero for y)
x - (0) = 5
x = 5
y-int(plug in zero for x)
(0) - y = 5
-y = 5
y = 5
200
Draw and a label a graph with zero slope and a graph with an undefined slope.
See individual answers.
Zero slope = horizontal line
Undefined = vertical line
200
Decide if the graph is a function.
Use the vertical line test.
Not a function
300
Without plotting the points, tell whether it is in Quadrant I, Quadrant II, Quadrant III or Quadrant IV.
A. (-4, -3)
B. (3, 2)
C. (1, -5)
A. (-4, -3) III
B. (3, 2) I
C. (1, -5) IV
300
The gallons G of water used to take a shower varies directly with the number of minutes M in the shower. A 7 minute shower uses 42 gallons of water.
I. Find an equation that relates the two variables.
II. Find out how many gallons you would use if you took a 9 minute shower.
y = k(x)
G = k(t)
42 = k(7)
k = 6
G = 6(t) t=9 minutes
G = 6(9)
G = 54 gallons
300
Graph the equation using slope-intercept form.
y + 1 = (1/2)x
y = (1/2)x - 1
m = 1/2
b = -1
300
Decide whether the graphs of the two equations are parallel lines without graphing.
y = x + 3, y = x + 6
Yes, the lines are parallel.
(Two lines with the same slope are always parallel. Both of these lines have a slope of 1 (m=1), so the lines are parallel. )
300
Decide whether the relation is a function.
Remember each input can one have only ONE output.
Not a function.
400
Scatter Plots! See attachment
See individual answers.
400
Find two ordered pairs that are solutions of the equation.
y = x - 5
Plug in numbers for x, get an output of y.
(-1, -6)
(0, -5)
(1, -4)
(2, -3)
(3, -2)....
400
Graph the equation using a table of values.
-3x + y = 8
See individual answers.
Steps:
1. Solve for y.
2. Plug in a few numbers for x, make an input/output chart.
3. Plot points/connect dots.
400
Find the slope of the line passing through the two points.
(-5, 2) (1, -4)
m = (-4-2)/(1--5) = -6/ 6= -1
400
Evaluate the function when x = 1 and x = 0.
g(x) = x -2
g(1) = (1) - 2
g(1) = -1
g(0) = (0) - 2
g(0) = -2
500
Find the x-intercept and y-intercept of the given graph.
(see attachment)
X = 1
Y = -3
500
Solve the equation algebraically. Check your solution graphically.
3x - 5 = 1
x = -2
Graph the equation. x-intercept should be x = -2.
500
Solve the equation graphically. Check your solution algebraically.
7 - 5x = -3
Check individual answers.
Steps to solve graphically:
1. Rewrite in form ax + b = 0 (get zero on one side of equal sign)
2. Rewrite in y = mx+b form. (replace zero with y)
3. Graph using slope-intercept. (plot b, use m to plot 2nd point)
4. Solution is the x-intercept.
Algebraically:
-5x = -10
x = 2
500
In 1990, a Michael Jordan autograph cost $550. In 2012, a Michael Jordan autograph cost $1200. Find the average rate of change in the value(cost) of a Michael Jordan autograph in dollars per year.
Whenever you see "rate of change," think slope.
slope = difference in cost / difference in time.
slope = $1200 - $550 / 2012 - 1990
slope = $650 / 22 yrs
slope = about $30/1yr.
So, each year, the price of a Michael Jordan autograph goes up about $30.
500
Graph the function.
f(x) = (1/2)x - 4
See individual answers.
Steps:
1. Replace f(x) with y.
2. Use slope-intercept form to graph. (b=-4, m=1/2)