Important Vocab
What is the term for the point where the graph crosses the x-axis?
Horizontal intercepts or intercepts
Given the equation y=3x+2, identify the slope and y-intercept.
Slope: 3, y-intercept: 2.
Find function of f(x) when we have f(12)=15 and f(5)=7
We have two points (12,15) and (5,7)
m=15-7/12-5
m=8/7
f(x)=8/7x+b
7=8/7(5)+b
7=40/7+b
7-40/7=b
49/7-40/7=b
b=9/7
System of equations
y=x
y=-x
(0,0)
On a graph, what is the term for the dependent variable?
Outputs, y values
How would you find the x-intercept and y-intercept of the line given by the equation 5x−2y=10?
set x=0
set y=0
The owners of an apartment building bought it new and then 9 years later sold it for $149000. They calculated that the building appreciated $5000 per year while they owned it.
How would you solve this?
do 149000-5000
finding value of the house year 8
144000-5000
finding value of the house year 7
plug points into desmos
use y1~mx1+b
(0,-4) the solution to the system y=-20x+1 and 20x+y=6
no
there is no intersection
If a graph is sloping upwards as you move to the right, is the function increasing or decreasing?
How can you identify a linear pattern from a table of values?
A linear pattern has a constant rate of change between the x-values and y-values (the difference between successive outputs is constant for equal intervals of input.)
Plug: f(x)=x^3-4x+3 into desmos
is it a function? How do you know?
yes, because if you preform the vertical line test, the line will not go through the same x twice
Isa thinks y=3x+4 and y=-x-4 has a solution. Michelle thinks there is not. Who is right?
Isa (-2,2)
Given a linear graph, how can you identify the horizontal and vertical intercepts?
When line passes through x-axis (horizontal) and y-axis (vertical)
Given a table with values:
x: 1, 2, 3, 4
y: 4, 6, 8, 10
Write the equation of the line that represents this pattern
y=2x+2
Plug in f(x)=3x-45 into desmos.
What is domain and range
D-(−∞,∞)
R-(−∞,∞)
The solution to the system x+y=2 and y=3
using subsitution
x+3=2
x=-1
y=3
Draw a qualitative graph representing someone walking at a constant speed.
Draw on board
A company’s profit is modeled by the equation y=6x−15 , where y is the profit in dollars, and x is the number of items sold. How many items must be sold for the company to have a profit of at least $30?
Extra 25pts- How many items sold will make them earn profit and how much do they make
x=7.5 ---> x=8
We can't sell half a product
x=3 y=$3
Given the function g(x)=3x−7, if g(a)=8, find the value of a
Set up the equation using the function definition: g(a)=3a−7
Set the function equal to 8:
3a−7=8Solve for a: 3a=15 --->a=15/3 ---> a=5
There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in all. How many of each animal are there?
There are 13 animals in total: C+P=13
There are 40 legs in total. Chickens have 2 legs each and pigs have 4 legs each: 2C+4P=40 Simplify by dividing by 2 so C+2p=20
Plug- C+P=13 and C+2p=20 to desmos