Algebra 1 Unit 4 Flashcards
What is rate of change?
A ratio that shows how one variable changes with respect to another
How is slope written?
As a ratio of the vertical change (Rise) to the horizontal (Run) between any two points on a line
Slope is the what for any two points on the same line?
It is the constant
Slope should be written how?
As a fraction in simplest form
What is the variable for slope?
M
What are the four types of slope?
Positive, Negative, Zero, and Undefined
The main formula for slope on a graph is …
M = Rise over Run
The slope formula when given two points is …
M = y - y over x - x
What is a linear equation?
It is a straight line (not a curve), and the x is not squared or cubed.
What are the three forms of a line?
slope-intercept, point-slope, standard
What is the point slope form?
y-y = m (x-x)
What is the slope intercept form?
y=mx+b
What is the standard form?
Ax+By=C
y-y=m(x-x) what form?
point slope
y=mx+b what form?
slope intercept
Ax+By=C What form?
standard
Why is it called “point-slope” form?
it has a hidden point and a slope in it
Why is it called “slope-intercept” form?
it has a slope and an intercept in it
How do you find the hidden point in point slope form? y-y=m(x-x)
to get your (x,y), take the opposite of the number next to the x to get your x, and take the opposite of the number next to the y to get your y
How do you find the points in Standard Form?
(0, __) and ( ,0).
use (0, ) to get the y intercept and (__,0) to get the x intercept.
How do you find the slope in Standard Form?
m = -A/B (opposite of A over B)
How can you find the y intercept in any form?
You can always just plug a zero in for x and then solve for y. (0, __).
How can you find the x intercept in any form?
You can always just plug a zero in for y and then solve for x. (__ ,0)
what do you call something that goes straight up and down?
VERTICAL
What dod you call something that goes from left to right?
HORIZONTAL (like looking along the horizon)
What is the name of the point (0,0) ?
origin
What does VERTICAL mean?
goes straight up and down
What does HORIZONTAL mean?
goes from left to right
What is the origin?
(0,0)
What is the equation of the x axis?
y=0
Wat is the equation of the y axis?
x=0
What if a linear equation is not in one of the three forms? What can you do?
use algebra to rearrange it
what form? y = 4x - 3
slope intercept
what form? y - 3 = 2( x-8)
point slope
what form? 4x-2y=7
standard
Whst is the point at which the line intersects the x-axis?
The x-intercept
Whst is the point at which the line intersects the y-axis?
The y-intercept
To find the x-intercept, what must you do?
Set y equal to zero and solve for x
To find the y-intercept, what must you do?
Set x equal to zero and solve for y
What are parallel lines?
Two lines that never intersect
What do paralell lines share in common?
They share the same slope
What are perpendicular lines?
Two lines that intersect at a 90 degree angle
How are peperndicular slopes linked?
They are negative (opposite) reciprocals
What are negative reciprocals?
A fraction “flipped” and the signs are “switched”
Whengiven a word problem, when do you use slope intercept form?
When given a rate of change (m) and a starting point (b)
Whengiven a word problem, when do you use standard form?
When the problem relates two different objects
Whengiven a word problem, when do you use point slope form?
When the problem gives a sample point (x,y) and rate of change (m).
Whengiven a word problem, when do you use point point point form?
When the problem gives two sample points
What is a Scatter Plot?
A graph that shows the relationship between two variables
How many types of relationships can a scatterplot have?
3
What are three correlations a scatterplot can have?
Positive, Negative, and None
What does a scatterplot allow you to do?
Plot data to make a prediction
