Moving Straight Ahead Students will work on linear equations, solving equations, solving inequalities, determining slopes and what they mean, and determining the intersection of 2 lines.

Investigation 1 In this unit students will review unit rates and relate them to linear relationships.

Vocab Linear Relationship all points lie on a straight line, a 1 to 1 relationship Dependent Variable the y-axis, depends on the value of another, output, answer Independent Variable the x axis, value does not depend on another, you control this, input

Homework Page 16 A 1, 4, 6, 10, 12, 13 B 7, 11, 12, 14, 31

Invest 1.1 What equations represent the relationship between the time and the distance you walk at a constant rate? What are the dependent and independent variables?

Lab – determine your walking rate Each square in the hallway is 12 inches Mark off 30 feet Do problem 1.1 on page 9 Use yards per second, answer questions in section B

Notes Using idea of unit rate and constant of proportionality Y=kx Better y=mx+b M is the slope or the unit rate in this case, does not need to be the unit rate, but it is a rate, be able to describe what the slope means m=change in y/change in x we will discuss more later Be able to write equation and know if you are subbing in value for x or y

Invest 1.2 How can you predict whether a relationship is linear from a table, a graph or an equation that represents the relationship?

Linear – straight line, how can you determine Graph Visual – can see it is a straight line Equation y=mx+b there is multiplication between the slope and the x or independent variable Table Pattern in the table, just like constant of proportionality, are you continually adding or subtracting the same value to the right and the left

Example is the relationship linear, explain

Graphing a linear relationship Make a table starting when x=0 and continue for at least 4 more numbers Calculate the y value – continually add the unit rate Plot the points on a graph For graph – make sure you have axis labeled, make sure you have a good scale for x and y axis

What is the pattern of change in a linear relationship? Invest 1.3 What is the pattern of change in a linear relationship?

Word Problems Can you write an equation, amount of money based on the number of kilometers walked? Is it linear? What is the b value in the equation y=mx+b

Writing an equation Y=mx+b M is the slope, rate of change, what is the value that you would constantly add or multiply by to get next value B do we start with something that won’t change, initial cost like charge to deliver a pizza no matter how many we order

Invest 1.4 How can you determine if a linear relationship is increasing or decreasing?

Recognizing Information based on linear graph, table or equation Start of the problem y-intercept, the b value, when x=0 What is done per slope, m, rise/run, rate Equation y=mx+b Increasing m is positive, values go up over x value increasing, up from left to right Decreasing m is negative, values go down over x value increasing, down from left to right

Example How much money is in the account at the start of the project? How much money is withdrawn from the account each week? Does this represent a constant of proportionality? Write an equation? Is this linear? Explain