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Contents Lesson 8-7Writing Linear Equations

Lesson 7 Contents Example 1Write Equations From Slope and y-Intercept Example 2Write an Equation From a Graph Example 3Write an Equation to Solve a Problem Example 4Write an Equation Given Two Points Example 5Write an Equation From a Table

Example 7-1a Write an equation in slope-intercept form for the line. Slope-intercept form Answer: Replace m with and b with 7.

Example 7-1a Write an equation in slope-intercept form for the line. Replace m with 0 and b with –3. Answer: Simplify. Slope-intercept form

Example 7-1a Write an equation in slope-intercept form for the line. Slope-intercept form Replace m with 2 and b with 0. Answer: Simplify.

Example 7-1b Write an equation in slope-intercept form for each line. a. b. c. Answer:

Example 7-2a Write an equation in slope-intercept form for the line graphed. The y -intercept is –4. From (0, –4), you can go up one unit and to the right one unit to another point on the line. So, the slope is 1.

Example 7-2a Slope-intercept form Replace m with 1 and b with –4. Answer: Simplify.

Example 7-2b Write an equation in slope-intercept form for the line graphed. Answer:

Example 7-3a Business The owners of the Good Times Eatery surveyed their customers to find out where they lived. They learned that for each 5-mile radius from their restaurant, 30 fewer people visited them. They had 150 patrons in the area immediately surrounding the diner. Write an equation to show the relationship between miles x and customers y. WordsNumber of customers decreases by 30 for each 5-mile increase in radius. VariablesLet x = miles and let y = customers.

Example 7-3a Step 1Find the slope m. EquationsUse. Simplify. decrease of 30 customers increase of 5 miles

Example 7-3a Step 2Find the y -intercept b. Slope-intercept form Replace m with –6 and b with 150. Answer: (x, y) = (distance, customers) = (0, b) When the distance is 0 miles, the number of customers is 150. So, the y-intercept is 150. Step 3Write the equation.

Example 7-3a Predict the number of customers who lived 20 miles away. Answer:At a distance of 20 miles, the number of customers is 30. Write the equation. Replace x with 20. Simplify.

Example 7-3b Weather Attendance at an outdoor sporting event is affected by the temperature outside. When the outside temperature is 0°F, the attendance is 12 people. For every increase in temperature of 20 degrees, the attendance increases by 100 people. a. Write an equation to show the relationship between temperature x and attendance y. b. Predict the attendance if the temperature is 60°F. Answer: 312 Answer:

Example 7-4a Write an equation for the line that passes through (7, 0) and (6, 3). Step 1Find the slope m. Definition of slope

Example 7-4a Step 2Find the y -intercept b. Use the slope and the coordinates of either point. Slope-intercept form Replace m with –3, x with 7, and y with 0. Simplify.

Example 7-4a Step 3Substitute the slope and y -intercept. Replace m with –3 and b with 21. Answer: Slope-intercept form

Example 7-4b Write an equation for the line that passes through (4, –2) and (–2, –14). Answer:

Example 7-5a Use the table of values to write an equation in slope-intercept form. xy –216 – –2 Definition of slope Step 1Find the slope m. Use the coordinates of any two points.

Example 7-5a Step 2Find the y -intercept b. Use the slope and the coordinates of either point. Slope-intercept form Replace m with –6, y with 16, and x with –2. Simplify. Step 3Substitute the slope and y -intercept. Answer: Slope-intercept form Replace m with –6 and b with 4.

Example 7-5b Use the table of values to write an equation in slope-intercept form. xy –64 –32 3–2 6–4 Answer:

End of Lesson 7

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