1. 4-3A Writing Equations in Slope-Intercept Form Algebra 1 Glencoe McGraw-HillLinda Stamper

2. In the previous lesson you wrote direct variation equations. In today’s lesson, when you know the slope and the y- intercept you will be able to write the equation of a line. The y-intercept is the y- coordinate of the point where the line crosses the y-axis. x y Do you remember y-intercept?

3. The linear equation y=mx+b is written in slope-intercept form where m is the slope and b is the y-intercept. slope y-intercept

4. If y = x + 3 then slope y-intercept the slope is and the y-intercept is Slope is a numerical value – do not include the variable x.

5. If y = 2x – 3 then slope y-intercept the slope is | –| – and the y-intercept is The slope is a numerical value – do not include the variable x.

6. How to write the equation of a line given the slope and the y-intercept. Write the slope-intercept form. Substitute the slope for m and the y-intercept for b. Simplify – undo the double sign. Write the equation of the line whose slope is 9 and whose y-intercept is –6.

7. Write an equation in slope-intercept form of the line with the given slope and y-intercept. Example 1 slope: 7, y-intercept: –2 Example 2 slope:, y-intercept: – 10

8. x y # of books Shipping costs (dollars) 1 2 24 An online store charges $3 per order plus $1.00 per book for shipping. Write a linear equation in slope-intercept to model the situation. 0 3 4 5 6 7 8 9 6 8 10 Let x represent number of books and y represent cost of shipping. 10 Find the y-intercept. Constant rate of change is slope. The charge per book is the slope, so m = 1.

9. Example 3 You want to rent a rowboat for a fishing trip. There is an initial fee of $25, plus a $50 daily fee. Write a linear equation for this situation where y represents the cost of renting a rowboat and x represents the number of days rented. Example 4 Jenny opened a savings account with $200 and plans on saving $100 per month. Write a linear equation for this situation where y represents the savings and x represents the number of months. Constant rate of change is slope.

10. x y # days Rental cost (dollars) 25 50 12 Example 3 You want to rent a rowboat for a fishing trip. There is an initial fee of $25, plus a $50 daily fee. Write a linear equation for this situation where y represents the cost of renting a rowboat and x represents the number of days rented. 0 75 100 125 150 175 200 225 3 4 5 Find the y-intercept. Constant rate of change is slope.

11. x y time (months) savings (sollars) (0,200) 100 12 Example 4 Jenny opened a savings account with $200 and plans on saving $100 per month. Write a linear equation for this situation where y represents the savings and x represents the number of months. 0 300 500 700 900 3 4 5 Find the y-intercept. Constant rate of change is slope.

12. Write 2x – y = -3 in slope-intercept form. The identify the slope and y-intercept. Write the equation. Rewrite in slope-intercept form (solve for y). Identify the slope and y-intercept. slope is 2 y-intercept is 3 1 You must write the variable term first. Copy the above in your spiral notebook!

13. Example 5 y-intercept is –2 Example 6 y-intercept is 2 Write the equation in slope-intercept form. Then identify the slope and y-intercept.

14. When a graph clearly indicates the y-intercept and another point on the line, you can use the graph to write an equation of the line. Recall that the y- intercept is the y- coordinate of the point where the line crosses the y-axis. x y

15. How to write the equation of a line given a graph. 1. Write the slope-intercept form. 2. Locate the y-intercept. 3. Locate another point on the graph to find the slope using the slope ratio. 4. Substitute slope and y-intercept in the slope intercept form. 5. Simplify if necessary (undo double sign and place negative out front).

16. Write the equation of the line shown in the graph using slope-intercept form. x y Write the slope-intercept form. Locate the y-intercept. Locate another point on the graph. Substitute the slope and y-intercept in the slope intercept form. Simplify - undo double sign. Use good form – place negative out front!

17. Write the equation of the line shown in the graph using slope-intercept form. x y Example 7 y-intercept -2 Example 8 x y y-intercept 3

18. Notice that the scales on the axes are different. In this case it would be difficult to calculate slope by walking the line (counting squares). Instead use the slope formula. x y 1 4 –1–1 –4–4 Scales on the axis different – use slope formula!

19. Example 9 Write the equation of the line shown in the graph using slope-intercept form. x y 1 4 –1–1 –4–4 Write the slope-intercept form. Locate the y-intercept. 8 Locate another point on the line. Write the coordinates of both points. (0,8) (–4,–4) Use the slope formula to calculate the slope. Substitute the slope and y-intercept in the slope intercept form.

20. Remember: Scales on the axis different – use slope formula to find the slope!

21. When the scales on the axes are different, you must use the slope formula. Could you use the slope formula if the scales are the same? x y 1 1 –1–1 –1–1 Yes, but it would be more work!

22. Write the equation of the line in the graph. x y What axis does the line intercept? y What is the y intercept? Write the equation.

23. Write the equation of the line in the graph. x y What axis does the line intercept? x What is the x-intercept? Example 10 Example 11 x y What axis does the line intercept? y What is the y-intercept?

24. Think of some coordinates. (0,1), (0,0), (0,–1), (0,2) Example 12 What special name is given to the graph of x = 0? x y y-axis

25. Example 13 What special name is given to the graph of y = 0? x y Think of some coordinates. (1,0), (0,0), (–1,0), (2,0) x-axis

26. 4-A5 Pages 207–208 # 12-23 and Handout A5.