MAT Algebra chapter 3-4 test
Solve the system using the substitution method. Check your solution. 7x + 8y = 28 x + 2y = -2
(12,-7)
Solve the system of equations by elimination. Check your solution. 1.3x + 1.2y = 1.6 0.3x + 0.2y = 0.6
(4,-3)
What is the slope intercept form for functions?
(x) = mx + b
What do you use for x values to graph the function?
-2, -1, 0, 1, 2
(-4, 7) (8, -2)
-3/4
(-11, 8) (6, 8)
0
If the 0 is on the top of the slope, what is the solution considered?
0
If possible, solve the system of equations using any method. 0.4x = 0.1y - 1.1 4x - y = 3
0 = 1.4 No solution
6x - 7y = 5 -12x + 14y = -10
0=0 Infinitely many solutions
Solve the absolute value equation. Check your solutions. |3 - 2x| = 10
3 - 2x = 10
If p(x) = 5x^2 + 6x - 2, find p(a + 1).
5a^2 + 16a + 9
What type of line do you write when the solution is undefined?
A vertical line
What is standard form?
Ax+By=C
f(x) = x2 + 6
D
G = {(82, -14), (14, 3), (-107, 3), (70, 47), (14, 9)}
D = {-107, 14, 70, 82} R = {-14, 3, 9, 47} Not a function because X = 14 repeats
D = {(0,0), (5, 13), (4, 14), (5, 0)}
D = {0,4,5} R = {0,13,14} Not a function because X = 5 repeats
What do you do after you get the variable eliminated?
Eliminate the same variable in multiple pairs of equations
A woman invested $9000 in two mutual funds. In one year part of her investment earned 4% simple interest and the other part earned 5% simple interest. At the end of that year, the woman had earned $407. How much did she invest at each rate?
F
What does f(x) mean?
F of X
What do you do first when solving systems with three equations and three unknowns?
Get one variable eliminated first
What type of line do you draw when the solution is 0?
Horizontal line
What can 2 lines do on a graph?
Intersect at a point (one solution) Never intersect (no solution) Same line (infinitely many solutions)
Find the slope of the line perpendicular to the line that passes through (4, 5/2) and (3, -1/2).
M = -1/3
Find the slope of the line parallel to the line that passes through (8, 8) and (22, 2).
M = -3/7
For the given equation, find the slope and the y-intercept. Use these to graph the equation. 5x + 3y = 6
M = -5/3 Y int = (0,2)
f(x) = -6x - 1
M = -6x Y int = (0,-1)
4x - 9y = -27
M = 4/9X Y int = 3
Are there any decimals or fractions in standard form?
No
Can A be negative?
No
y = -x + 1 x + y = -5/2
No solution
Where are X and Y in standard form?
On the left
Against the wind a commercial airline in South America flew 588 miles in 3.5 hours. With a tailwind the return trip took 3 hours. What was the speed of the plane in still air? What was the speed of the wind?
P = 182 MPH W = 14 MPH
y = 3/5x - 1/5 5x + 3y = -10
Perpendicular
What do you do when f(x) = a number?
Plug in whatever is in parenthesis of x
The sum of two numbers is 73. If four times the smaller number is subtracted from the larger number, the result is 18. Find the two numbers.
S = 11 L = 62
What happens if shifted L or R, or inside absolute value?
Shift the points accordingly * opposite of whatever number is added or subtracted inside the parentheses or absolute value
h(x) = 2/5x - 4
Slope = 2/5 Y int = -4
Find the slope (grade) of a snowboard trail that rises 64 feet vertically over a horizontal distance of 80 feet.
Slope = 4/5
What are the steps to graphing linear equations?
Solve for y Graph the line Shade
What do you do after that same variable has been eliminated?
Solve the system that is left (2x2) sytems
Line m passes through (-3, -5) and (1, 7), while line n passes through (-2, -10) and (2, 2). Are these two lines parallel? Explain why or why not.
They're parallel because they have the same slope
(-2/3, 4) (-2/3, 9)
Undefined
If the 0 is in the bottom of the slope, what is the solution considered?
Undefined
g(x) = x - 7
V shape Shifts right 7
When do you shade above?
When it's greater than
When do you shade below?
When it's less than
When do we write a dotted line?
When it's not a "or equal to"
When do you draw a solid line?
When it's or equal to
How do you do real world problems?
Write 2 equations Solve the system Answer the question
Find an equation of the line perpendicular to 4x - 2y = 10 and passing through (9, -1) in standard form.
X + 2y = 7
Find an equation of the line parallel to x = 3y - 8 and passing through (5, -2). Express the equation in standard form.
X - 3y = 1
What must happen for an equation to be a function?
X cannot repeat
y = -2/3x - 6 4x + 6y = -5
Y = -2/3x - 5/6
Determine whether each pair of lines is parallel, perpendicular, or neither. 2x + 5y = 35 5y + 2x = 16
Y = 2/5x + 7 Y = -2/5x + 16/5 Neither
What is a range?
all possible y values
If g(x) = 11 - x2 , find g(3).
g(3) = 2
What is substitution?
get a variable by itself and fill into the other equation
What is elimination?
nice columns with one column having opposite values
What do perpendicular lines have?
opposite reciprocal slopes
What do parallel lines have?
same slope
What does M mean?
slope
What is a domain?
x values
(4, 9), (-2, 5)
y = 2/3x + 19/3
Find the equation of the line passing through the given pair of points. Write the equation in slope-intercept form. (-5, -2), (2, 1)
y = 3/7x + 1/7
Write the slope-intercept form of each line, then state the slope and y-intercept. 4x-y=3
y = 4x - 3 Slope = 4x Y-int = -3
What does B mean?
y-intercept
What is point slope form?
y-y1=m(x-x1)
What is the formula for the slope?
y2-y1/x2-x1 Rise over run
What is slope intercept form?
y=mx+b
