Math Review

Write an inequality to show scale factors that reduce a shape?

0<k<1

What is a reflection? Write the algebraic rule for reflecting over the x-axis. Write the algebraic rule for reflecting over the y-axis.

A flip on the coordinate plane. Reflection over the x-axis; (x,y) -- (x,-y). A reflection over the y-axis (x,y)--(-x,y)

What are the 3 rules for standard form?

A is non-negative;A,B,&C are integers; A,B,C have a GCF of 1

Definition of function.

A relation where each x paired with exactly one y

What is a translation?

A slide (vertical, horizontal, or combination movement) on the coordinate plane.

What is a rotation? Write the algebraic rule for a 90 degree clockwise, 90 degree counterclockwise and 180 degree rotation about the origin.

A turn on the coordinate plane. 90 degree clockwise (same as 270 counterclockwise): (x,y)--(y,-x) 90 degree counterclockwise ( same as 270 clockwise); (x,y)-- (-y,x) 180 degree : (x,y)--(-x,-y)

What should the answer to a system look like?

An ordered pair (intersection point)

Definition of relation.

Any set of ordered pairs

How do you use the vertical line test to tell if a graph is a function?

As the vertical line passes over the graph, the vertical line can only intersect the graph one time.

What is the standard form of a line?

Ax+By=C

What must you do if you multiply or divide both sides of an inequality by a negative number?

Change the inequality sign

What is the rate of change formula? Rate of change is the same as

Difference in the dependent variable over the difference in the independent variable slop in the context of word problem.

How do you find the line of best fit on a graph and from a table?

Graph-draw a line that goes through as much data as possible and splits any remaining data evenly. Table (using a graphing calculator)- STAT, enter the ordered pairs, STAT, right arrow (CALC), 4 (LinReg), Enter

What are some ways to solve a system?

Graphing, Substitution, and Elimination

For linear inequalities, if is greater than, where do you shade? Less than?

Greater than=shade above, Less than=shade below

What's the short cut for recognizing a function in ordered pair form?

If you notice that there is an x value repeated with a different answer for the y value.

What is the rule to multiplying tow powers with the same base?

Keep the base, add the exponents

What is the rule of dividing two powers withe the same base?

Keep the base, subtract the exponents

Describe how to write an algebraic proof when solving and equation. Name the properties of equality.

Make a two column chart with statements and reasons. The first statement is the original problem and the reason is given. Each step of the work should be shown ad a property (numeric or equality) listed as the reason for the work. Properties of equality; Addition, Subtraction, Multiplication, or Division.

If absolute value equation is equal to a negative, what is the answer?

No solution

Define rational numbers

Numbers that can be written as the ratio of two integers (in decimal form, they repeat or terminate)

Define irrational numbers

Numbers that cannot be written as the ratio of two integers

What is true about the slopes of a parallel lines? Their y-intercepts

Parallel line have the same slopes, but different y-intercepts.

What is true about the slopes of perpendicular lines? Their y-intercepts?

Perpendicular line have slopes that are both opposite and reciprocal and can have the same or different y-intercept.

What word indicates to use parenthesis when translating a verbal sentence into an algebraic one?

Quantity

If given two points, how do you use your calculator to get the equation.

STAT, enter the ordered pairs, STAT, right arrow (CALC), 4(LinReg), Enter

When will a system have infinitely many solutions?

Same line (coinciding lines)

How do you find the x and y-intercepts of an equation?

Substitute 0 for y and solve for x. Substitute o for x and solve for y.

If you are given a point and a slope, explain how to find the equation.

Substitute the x,y, and m and solve for b. Write the equation using m and b

What is a dilation? Write the algebraic rule.

The enlargement or reduction of a figure, (x,y)-- (kx,ky)

How can you tell if a graph,table, or equation is showing a linear model?

The graph shows a line, the table shows consistent numbering for the x values and repeated addition (or subtraction) of the same number for the y values, the equation can be written as slope-intercept form y=mx+b (the exponent of x must be one) or be a special linear equation x= a number or y=a number

What is the slope of a vertical line?

Undefined

When is it best to use your graphing calculator to solve a system?

When both equations are in slope-intercept form

Explain how to change 0.5(continuing) into a fraction

Write two equations that can be subtracted to convert the repeating decimal into a fraction. Let x-0.5(repeating)(The first equation needs to have the decimal in front of the repeating numbers. Let 10x-5.5(repeating)(The second equation needs to have the decimal after the repeating numbers. When you subtract the second and first equations, the results is 9x+5. Solve for x, x =5/9

What letter is the domain? Range? Output? Input? Independent variable? Dependent variable?

X=Domain, Input, and Independent Variable Y=Range, Output, and Dependent Variable

What keys do you press on your graphing calculator to solve a system.

Y=, enter equation, 2nd TRACE (Calc), 5 (intersection), ENTER,ENTER,ENTER. If graph does not show intersection point, adjust window

What is the slope of a horizontal line?

Zero

What is the Percent of change formula?

difference/original=%/100

Slope

is the ration of the rise to run

Write an inequality to show scale factors that enlarge a shape?

k>1

What does m and b stand for?

m=slope, b=y intercept

When will a system have no solution?

parallel lines

What is the special equation of and undefined line?

x=any number

How do you find "k"?

y divided by x

What is the Slope Formula?

y sub2- ysub1 over xsub2-xsub1

What is the special equation of a zero sloped line?

y=any number

What is the direct variation formula? What letter represents the constant of variation?

y=kx; k is the constant of variation ( k is the slope in a direct variation equation)

What is the slope-intercept form of a line?

y=mx+b