Writing Equations
What do you use in an equation when a number is unknown?
A variable
What does it mean to solve an equation?
To isolate the variable, find the value of the variable that makes the equation true
For the ordered pair (6, 7), what is the y-value?
y = 7
If you have 2 different points, what should you label them to find the rate of change?
(x1, y1) and (x2, y2)
What is slope-intercept form?
y = mx + b
How would you write "24 less than x"
x - 24
What are the 3 different possibilities for the number of solutions to an equation?
No solution, one solution, infinite solutions
What is the difference between a discrete vs. a continuous function?
A discrete function is individual points, a continuous function is a connected line or curve
What is the formula for rate of change?
(y2 - y1)/(x2 - x1)
What is the difference between m and b in slope-intercept form? (be specific!)
m is the slope, it is how the line Moves between points
b is the y-intercept, it is where the line Begins on the y-axis
What does the word "yields" mean?
Equal to
Solve: x + 2 = -14 - x
x = -8
What are all of the synonyms for independent variable?
Input, domain, x-value
If a graph is measuring school attendance throughout the month of October and the rate of change is negative, what does that mean in the context of the situation?
Attendance is decreasing over time
Describe the graph of y = -2x - 7
The graph has a y-intercept of (0, -7) and goes down 2 right 1 in between points
How would you write "3 multiplied by the difference of x and 4"
3(x - 4)
Solve: 3|y - 12| = 24
y = {4, 20}
If f(x) = x2 - 3x + 1, what is f(4)?
f(4) = 5
Find the value of r if the rate of change between (6, r) and (5, -4) is -2.
r = -6
What is the equation of the line that has a slope of 5 and passes through the point (1, -2).
y = 5x - 7
The perimeter of a rectangular patio is 100 feet, the width of the patio is 8 feet, and the length is 3(x+2) feet. What is the equation to solve for x?
100 = 2(8) + 2(3(x+2))
How many solutions does the following equation have:
2x + 3(x - 2) = 6x - 2(x + 3) + x
Infinite solutions
Identify and interpret the y-intercept in the table of values
For the graph of g(t), find the rate of change on the interval [1, 3]
rate of change = 2
Convert to standard form:
2x - 3y = 12
y = (2/3)x - 4