Splash Screen

Five-Minute Check (over Lesson 8–7) Then/Now New Vocabulary Example 1: Write the Equation of a Line in Slope- Intercept Form Example 2: Write an Equation Given Two Points Example 3: Write an Equation from a Table Example 4: Real-World Example: Write an Equation to Make a Prediction Concept Summary: Write a Linear Equation Lesson Menu

Find the slope and y-intercept for the graph of y = x + 5. A. slope = 2; y-int = 5 B. slope = 1; y-int = 5 C. slope = 1; y-int = –5 D. slope = 2; y-int = –5 5-Minute Check 1

Find the slope and y-intercept for A. slope = ; y-int = –3 B. slope = 2; y-int = –3 C. slope = 2; y-int = 3 D. slope = ; y-int = 3 5-Minute Check 2

Find the slope and y-intercept for the graph of x + y = 4. A. slope = 1; y-int = 4 B. slope = 1; y-int = –4 C. slope = –1; y-int = –4 D. slope = –1; y-int = 4 5-Minute Check 3

Graph y = 3x + 1 using the slope and y-intercept. A. B. C. D. 5-Minute Check 4

The printer charged a flat rate of $65 The printer charged a flat rate of $65.00 to print invitations, plus an additional charge of $0.15 per invitation for the art on them. Which equation shows the total cost t of buying x invitations? A. t = 0.15x B. t = 65x + 0.15 C. t = 0.15x + 65 D. t = 65x + 1 5-Minute Check 5

Which of the following is 3x + 2y = 6 in slope-intercept form? A. B. C. D. 5-Minute Check 6

Use linear equations to solve problems. You have already graphed linear equations using the slope and y-intercept. (Lesson 8–6) Write equations given the slope and y-intercept, a graph, a table, or two points. Use linear equations to solve problems. Then/Now

point-slope form Vocabulary

y = mx + b Slope-intercept form Write the Equation of a Line in Slope-Intercept Form A. Write an equation in slope-intercept form for the line with slope and y-intercept 7. y = mx + b Slope-intercept form Answer: Example 1 A

B. Write an equation in slope-intercept form for the line graphed. Write the Equation of a Line in Slope-Intercept Form B. 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 1 B

y = mx + b Slope-intercept form Write the Equation of a Line in Slope-Intercept Form y = mx + b Slope-intercept form y = 1x + (–4) Replace m with 1 and b with –4. y = x – 4 Simplify. Answer: y = x – 4 Example 1 B

A. Write an equation in slope-intercept form for the line with slope –3 and y-intercept –5. A. y = –3x + 5 B. 3x + y = –5 C. y = –5x – 3 D. y = –3x – 5 Example 1 CYP A

B. Write an equation in slope-intercept form for the line graphed. Example 1 CYP B

Write an Equation Given Two Points Write an equation for the line that passes through the points (7, 0) and (6, 3). Step 1 Find the slope m. Definition of slope (x1, y1) = (7, 0) (x2, y2) = (6, 3) Simplify. Example 2

y – y1 = m(x – x1) Point-slope form Write an Equation Given Two Points Step 2 Use the slope and the coordinates of either point to write the equation in point-slope form. y – y1 = m(x – x1) Point-slope form y – 0 = –3(x – 7) Replace (x1, y1) with (7, 0) and m with –3. y = –3x + 21 Simplify. Answer: y = –3x + 21 Example 2

Write an equation for the line that passes through (4, –2) and (–2, –14). A. y = –8x + 30 B. C. y = 2x + 6 D. y = 2x – 10 Example 2 CYP

Step 1 Find the slope m. Use the coordinates of any two points. Write an Equation From a Table Write an equation of the line in point-slope form that passes through the points shown in the table. Step 1 Find the slope m. Use the coordinates of any two points. Definition of slope (x1, y1) = (–2, 16) (x2, y2) = (–1, 10) Simplify. Example 3

y – y1 = m(x – x1) Point-slope form Write an Equation From a Table Step 2 To write the equation, use the slope and the coordinates of any point. y – y1 = m(x – x1) Point-slope form y – (–2) = –6(x – 1) Replace (x1, y1) with (1, –2) and m with –6. y + 2 = –6(x – 1) Simplify. Answer: The equation is y + 2 = –6(x – 1) or y = –6x + 4. Example 3

Use the table of values to write an equation in slope-intercept form. D. Example 3 CYP

Write an Equation to Make a Prediction BUSINESS The number of customers living within 5 miles of a restaurant is 150. The number of customers decreases by 30 for every 5 miles beyond the original 5-mile radius. Estimate the number of customers who live between 15 and 20 miles away. Understand You know the rate of change of number of customers to each 5-mile radius (slope) and the number of customers in the area immediately surrounding the restaurant (y-intercept). Make a table of ordered pairs. Example 4

Write an Equation to Make a Prediction Plan Write an equation to show the relationship between the distance x and the number of customers y. Then, substitute the distance of 20 miles into the equation to find the number of customers. Solve Find the slope m. decrease of 30 customers increase of 5 miles Example 4

(x, y) = (distance, customers) = (0, b) Write an Equation to Make a Prediction Find the y-intercept b. (x, y) = (distance, customers) = (0, b) When the distance is 0 miles, the number of customers is 150. So, the y-intercept is 150. Write the equation. y = –6x + 150 Example 4

Substitute the distance of 20 miles. Write an Equation to Make a Prediction Substitute the distance of 20 miles. y = –6x + 150 Write the equation. y = –6(20) + 150 Replace x with 20. y = 30 Simplify. Answer: At a distance of 20 miles, the number of customers is 30. Example 4

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. Predict the attendance if the temperature is 60°F. A. 112 people B. 300 people C. 312 people D. 412 people Example 4 CYP

Concept

End of the Lesson