Chapter 4 Section 1 Essential Question How can we model relationships between quantities? Common Core State Standards: 8.F.4 Mathematical Practices: 1, 3, 4, 5

Real World Link – Page 267 Space – The following table shows the total distance d that the space shuttle covers in certain periods of time t. Time (seconds) Distance (miles)

Real World Link – Page Write an algebraic expression for the distance d in miles for any number of seconds t. Time (seconds) Distance (miles)

Real World Link – Page Write an algebraic expression for the distance in miles for any number of seconds t. Answer: 5t Time (seconds) Distance (miles)

Real World Link – Page Write an algebraic expression for the distance in miles for any number of seconds t. Answer: 5t 2. Describe the relationship in words. Answer: the distance is 5 times the number of seconds.

Real World Link – Page Graph the ordered pairs. Describe the shape of the graph. Time (seconds) Distance (miles)

Real World Link – Page Graph the ordered pairs. Describe the shape of the graph. Answer: a line Time (seconds) Distance (miles)

Tables, Graphs and Equations An equation is a mathematical sentence that that two quantities are equal. A linear equation is an equation with a graph that is a straight line. Some equations contain more than one variable.

Examples 1-2 pg 268 Example 1 Use the table to write an equation to find the number of liters in any number of quarts then describe the relationship in words. Quarts, Q Liters, L

Examples 1-2 pg 268 Difference in quart values: 2-1 = 1, 3-2 = 1, 4-3 = 1, 5-4 = 1 Difference in liter values: =.95, =.95, 3.8 – 2.85 =.95, 4.75 – 3.8=.95 Constant rate of change is.95 liters/1 quart L =.95Q Quarts, Q Liters, L

Examples 1-2 pg 268 o L =.95Q o About how many liters are in 8 Quarts. o L =.95(8) = 7.6 o There are about 7.6 liters in 8 quarts

Got It a and b pg 268

Examples 3-4 pg Using the graph, write an equation to find the number of miles run y after any number of days x. Step 1: Find the slope Step 2: Find the y-intercept Step 3: Use the slope – intercept form of a linear equation.

Examples 3-4 pg 269

Using the graph, write an equation to find the number of miles run y after any number of days x. Step 1: Find the slope 7/2 or 3.5 Step 2: Find the y-intercept 0 Step 3: Use the slope – intercept form of a linear equation. y = 3.5x + 0

Examples 3-4 pg 269 y = 3.5x How many miles will Marion run after 2 weeks? 2 weeks = 14 days y=3.5(14) + 0 y=49 miles Marion will run 49 miles in 2 weeks (14 days).

Got it c and d pg 270

Multiple Representations of Linear Equations pg 270 WordsEquations TableGraph All can be used to represent linear relationships

Examples 5-6 pg 271

Got it e and f pg 271

Guided Practice Pg 272

B B

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D D

A A