Standard Form & Intercepts
Find the y-intercept of the linear equation
2x + 3y = 12
(0,4)
Calculate the slope of the line passing through (2, 3) and (6, 11)
m=2
A car travels 150 miles in 3 hours at a constant speed. What is the average rate of change in miles per hour
50mph
Write a standard form equation for spending budget of $50 x tshirts at $10 each and y shorts at $5 each
10x + 5y = 50
The equation y2 minus y1 over x2 - x1 is called the
slope formula
Find both the x-intercept and y-intercept of
-4x + 5y = 20 as coordinate pairs.
x intercept (-5,0) and y intercept (0,4)
Calculate the slope of the line passing through (-3, 7) and (1, -5)
m= -3
A water tank contains 80 gallons 2 minutes and 50 gallons at 7 minutes. Calculate the rate of change with proper units
-6 gallons a minute (draining)
An event venue change a flat fee plus a cost per guest. If 20 guest cost $250 and 50 guest cost $550, find the cost per guest (slope)
$10 per guest
The slope of a line can have units and represent a ______ ______ _______ of variables
rate of change
A club sells adult tickets x for $8 and student tickets y for $5 to reach a goal of $400. Write the equation in standard form
Equation: 8x + 5y = 400
Prove that calculating the slope between (-1, 4) and (3, -2) gives the exact same result regardless of subtraction order2
m= -3/2 or m= -1.5
Interpret what a slope of m = -15 represents when y is bank balance in dollars and x is time in weeks
The bank balance decreased by $15 a week
A budget constraint is 3x + 6y = 300 for chicken (x) and beef (y). Find if 40lb of chicken and 25 lbs of beef is possible within the budget.
Yes it is within the budget because 270 is less than 300
Ax + By= C is called the _______ of linear equation
Standard Form
Identify the x- and y-intercepts of 3x - 4y = 12 and explain how to use them to graph the line
Intercepts are (4,0) and (0,-3). Plot both points on the coordinate plane and draw a line passing through them
Given the table values x: 0, 3, 6, 9; y: 10, 8, 6, 4 calculate the rate of change and state if the function is increasing or decreasing
-2/3
Decreasing
Runner A's distance is modeled by d = 6t meters per second. Runner B passes (2, 10) and (6, 22) meters per second. Who runs faster and by how much?
Runner A is faster by 3 meters per second
At an amusement park 4 rides cost $18 and 10 rides cost $33. Calculate the ticket price
Each ticket price cost $2.50
Ax + By C when you substitute x=0 and y=0 you are solving for what two things. Be specific
When you plug in 0 for x you get the y intercept
When you plug in 0 for y you get the x intercept
Consider an equation in standard form Ax + By = C
where A is equal to zero, B and C are not zero. What line would this represent?
horizontal line
A line passes through (4, r) and (8, 10) with a slope of m = 3/2 . Solve algebraically for r
r= 4. The point is (4,4)
A hiker ascends from 1,200 ft 8 AM to 3,600 ft at 11 AM, rests until 12 PM, then reaches 4,200 at 1 PM. Compare the rates of change for each leg
Leg 1: 800 feet per hour
Leg 2: 600 feet per hour
Leg 1 was the steepest out of all the legs
A theater sells $20 floor seats and $12 balcony seats with a goal of 1200. Identify two points that would satisfy this scenario . Write your answer is standard form and provide two solutions
answer may vary
possible answer(60,0), (30,50), (0, 100)
an equation that can be written in the standard form of a linear equation
linear equation in two variable