Slope and Rate of Change
What is the formula for to find the slope?
(y2 - y1) / (x2 - x1)
What is the slope-intercept form equation?
y = mx + b
What is the standard form equation?
Ax + By = C, A and B cannot 0
What is the point-slope form equation?
y - y1 = m (x - x1)
What is the basic description of an absolute value graph?
a "v" shaped graph pointing up or down
What is the slope of a vertical line, and what does it's equation look like?
slope: undefined
x = #
Find the slope and y-intercept of the following:
y = (4/3)x - 3
m = (4/3); up 4, right 3
b = -3; (0,-3)
What makes standard form special? And how do you use it?
You are able to find both x- and y- intercepts. Substituting 0 for x and solve for y; and 0 for y and solve for x
How do you know if a line in parallel or perpendicular to another line?
Parallel: same slope, different y-intercept
Perpendicular: slopes are negative reciprocal (flip numerator & denominator and opposite signs)
How do you know if the graph opens upward or downward?
If there is a negative sign in from of the absolute value sign it opens downward (mountain shape). If there is not a negative sign then the graph opens upward (valley shape)
Find the slope between the following 2 point:
(3 , -2) & (-5 , -4)
1/4
Graph the following equation:
y = (2/3)x - 4
Start at (0,-4); then move up 2, right 3.
GRAPH
Find the intercepts and graph:
6x + y = 12
(0,12) & (2,0)
GRAPH
Write the equation in slope-intercept form of a line that goes through the following 2 points:
(-1,0) & (-3,-1)
y = (1/2)x + 1/2
Explain the different ways the absolute value graph and move, and how do you know which way it will move?
Outside the symbols is an up/down movement; (+) is up & (-) is down.
Inside the symbols is left/right movement; (+) moves left & (-) moves right.
Find the rate of change for the following situation:
A plant measures .5in at the end of week 1, and 14in at the end of week 5
3.375 in/wk
Graph the following:
-2y = 5x - 12
Start at (0,6); then move down 5 right 2
GRAPH
Find the intercepts and graph:
4x - 3y = 12
(0,-4) & (3,0)
GRAPH
Write an equation in slope-intercept form of a line goes through the points:
(4,3) & (-2,1)
y = (1/3)x + (5/3)
Graph the following:
y = -|x+2| + 4
Reflection point is (-2,4), opens downward
GRAPH
Find the rate of change for the following situation:
A kitten grows from 5oz at birth to 3lb 5oz at 6 months
8oz/month
Write an equation in slope intercept for the following situation:
An airplane with no fuel weighs 2575 lbs. Each gallon of fuel added to the fuel tank weighs 6lbs.
y = 6x + 2575
Write an equation in standard form for the following situation:
You have $25 to buy supplies for a class party. Juice costs $3/bottle and chips cost $2/bag.
3j + 2c = 25
Write two equations in slope-intercept form, one that is parallel to and one perpendicular to y = 5x - 2, and going through (5,-1).
Parallel: y = 5x - 26
Perpendicular: y = (1/5)x - 2
Graph the following:
y = |2x - 3| - 2
Reflection point (1.5 , -2), opens upward with slope of lines 2 & -2
GRAPH