Graphing
Graph y = 2x + 3 on a coordinate plane. Plot / Label at Least three points
m = 2
b = 3 --> (0,3)
up 2 right 1 OR down 2 left 1 for rest of points
Write the equation of a line going through the (0,-4) points and (5, 2) in slope-intercept form.
slope: (y2 - y1) / (x2 - x1)
points: (0,-4) and (5,2)
slope: 6/5
y intercept (when x = 0): (0,-4)
y = 6/5x - 4
Mr. Orders needs to buy dog food for Sandie while grocery shopping. Sandie likes 2 different brands of dog food, Brand A that costs $20 a bag and Brand B that costs $12 a bag. Mr. Orders has a budget of $200 for groceries this week. Write an equation to model this situation if x represents the number of Bags of Brand A, and y represents the number of Bags of Brand B.
200 = 20x + 12y
Draw an Example of a Graph with a positive slope and a negative y intercept.
Slope goes up and to the right (or down and to the left) and passes through a negative y intercept.
Graph x = 3 on a coordinate plane
Vertical line passing through x = 3 (VUX)
Write the equation of the line represented by the table in slope intercept form:
____
x | y
0 | 1
2 | 3
4 | 4
6 | 5
_____
y intercept: 1
slope: pick any two points
y2 - y1 / x2 - x1
m = 1
y = x + 1
Mr. Orders needs to buy dog food for Sandie while grocery shopping. Sandie likes 2 different brands of dog food, Brand A that costs $20 a bag and Brand B that costs $12 a bag. Mr. Orders has a budget of $200 for groceries this week. Find the x intercept of this equation. What does the x intercept represent in the context of the problem?
x intercept ( y = 0)
20x + 0 = 200
20 x = 200
x = 10 bags of Brand A can be purchased if Mr. Orders buys 0 bags of Brand B.
Which of the following equations are equivalent? Explain.
y = 4x+9
2y + 4x = 12
y - 21 = 4(x-3)
y = 4x + 9 and y - 21 = 4(x - 3)
solve y - 21 = 4(x-3) for y.
Graph y = -5 on a coordinate plane.
horizontal line passing through y = -5
(HOY)
Write the equation of a horizontal line passing through the point (-4, 3).
horizontal line (HOY)
y = 3
Mr. Orders needs to buy dog food for Sandie while grocery shopping. Sandie likes 2 different brands of dog food, Brand A that costs $20 a bag and Brand B that costs $12 a bag. Mr. Orders has a budget of $200 for groceries this week. If Mr. Orders buys 4 bags of Brand A, how many bags of Brand B can he buy?
20x + 12y = 200
x = 4
Solve for y
20(4) + 12y = 200
80 + 12y = 200
12y = 120
y = 10 bags of Brand B.
Create a Table of Values that represents a horizontal line. How do you know?
x values can be anything
y values must be the same value / not change
Graph 2x - 3y = 18 on a coordinate plane. Graph at least 3 points
x intercept (y = 0) --> 2x = 18 (9,0)
y intercept (x = 0) --> -3y = 18 (0, -6)
OR change to y = mx + b
y = (-2/3)x -6
Write the equation of the line with a slope of 3 and passing through the points (4, -3) in ANY FORM
y + 3 = 3(x-4)
OR
y = 3x - 15
Mr. Orders' Roommate gave him a Starbucks gift card for his birthday worth $250. He spends $18.50 each time he goes to Starbucks (coffee is expensive, sue him). If x represents the number of times Mr. Orders has been to Starbucks and f(x) represents the total amount of money left on the card, write an equation to represent this situation in function notation.
f(x) = 250 - 18.5x
f(x) is just replacing y! (Just like last unit)
Adam believes that 12y + 2x = 24 and 36y + 6x = 72 are equivalent? Is he correct? Why?
Adam is correct! Set equal to y and solve!
y = -1/6x +2
Graph y - 1 = 1/2(x+4) on a coordinate plane. Plot / Label at least three points.
POINT SLOPE FORM!
Point (-4,1)
Slope: 1/2
use starting point and slope to graph rest
OR change to y = mx+b
y = 1/2x + 3
Write the equation of a line going through the points (2,3) and (-5,17) in slope-intercept (SI) form.
Slope: (17 - 3) / (-5 - 2) = 14 / -7 = -2
USE POINT SLOPE FORM AND TURN INTO Y = mx+b
Which point do you pick? You can use either!
y - 3 = -2(x-2) OR y - 17 = -2(x+5)
both get you y = -2x + 7
Mr. Orders' Roommate gave him a Starbucks gift card for his birthday worth $250. He spends $18.50 each time he goes to Starbucks (coffee is expensive, sue him). If x represents the number of times Mr. Orders has been to Starbucks and f(x) represents the total amount of money left on the card, how many trips to Starbucks will it take before Mr. Orders has $28 dollars left on the card?
f(x) = 28
28 = 250 - 18.50x
-222 = -18.5x
x = 12 trips to Starbucks
Create a Table of Values that Represents a Linear Equation. How do you know?
x values increase by same value each time
y values increase by same value each time
values that they increase by can be different from each other