X & Y Intercept Notes (Pg. 4)

2. X & Y Intercept Notes (Pg. 4)

3. Let’s do a review from Friday

4. Using Slopes and Intercepts 12-3 3y 3 4 –4x 3 3 4 9 3 = + 3 4 y =- x + 3 m =- 3 The slope of the line 4x+ 3y = 9 is – , and the y-intercept is 3. Course 3 Write each equation in slope-intercept form, and then find the slope and y-intercept. 4x + 3y = 9 4x + 3y = 9 –4x–4x Subtract 4x from both sides. 3y = 9 – 4x Rewrite to match slope-intercept form. 3y = –4x + 9 Divide both sides by 3. The equation is in slope-intercept form. b = 3

5. Shortcut method 4x + 3y = 9 To find slope, we take Opposite A B To find y-intercept, we take C B Plug into y = mx + b y = x + -4/3 9/3 = 3 -4/3 3

6. Using Slopes and Intercepts 12-3 Course 3 You can graph a linear equation easily by finding the x-intercept and the y-intercept. The x-intercept of a line is the value of x where the line crosses the x-axis (where y = 0). The y-intercept of a line is the value of y where the line crosses the y-axis (where x = 0).

7. Let’s see about graphing when given the x & y intercepts • Plot each intercept • Draw the line

9. Using Slopes and Intercepts 12-3 Remember This The form Ax + By = C, where A, B, C are real numbers, is called the Standard Form of a Linear Equation. Course 3

10. Using Slopes and Intercepts 12-3 4x = 12 4 4 Course 3 Additional Example 1: Finding x-intercepts and y-intercepts to Graph Linear Equations Find the x-intercept and y-intercept of the line 4x – 3y = 12. Use the intercepts to graph the equation. Find the x-intercept (y = 0). 4x – 3y = 12 4x – 3(0) = 12 4x = 12 x = 3 The x-intercept is 3. (3, 0)

11. Using Slopes and Intercepts 12-3 = –3y 12 –3 –3 Course 3 Additional Example 1 Continued Find the y-intercept (x = 0). 4x – 3y = 12 4(0) – 3y = 12 –3y = 12 y = –4 The y-intercept is –4. (0, -4)

12. Using Slopes and Intercepts 12-3 Course 3 Additional Example 1 Continued The graph of 4x – 3y = 12 is the line that crosses the x-axis at the point (3, 0) and the y-axis at the point (0, –4). Can we write slope-intercept form of this equation? m = 4/3 b = -4 y = 4/3x - 4 What do you think would happen if we changed Standard form like we learned last week?

13. Using Slopes and Intercepts 12-3 2x = 10 2 2 Course 3 Check It Out: Example 1 Find the x-intercept and y-intercept of the line 2x + 5y= 10. Use the intercepts to graph the equation. Find the x-intercept (y = 0). 2x + 5y= 10 2x + 5(0) = 10 2x= 10 x = 5 The x-intercept is 5. (5, 0)

14. Using Slopes and Intercepts 12-3 5y 5 = 10 5 Course 3 Check It Out: Example 1 Continued Find the y-intercept (x = 0). 2x + 5y= 10 2(0) + 5y= 10 5y= 10 y = 2 The y-intercept is 2. (0, 2)

15. Using Slopes and Intercepts 12-3 Course 3 Check It Out: Example 1 Continued The graph of 2x + 5y = 10 is the line that crosses the x-axis at the point (5, 0) and the y-axis at the point (0, 2). Can we write slope-intercept form of this equation? m = -2/5 b = 5 y = -2/5x + 5 What do you think would happen if we changed Standard form like we learned last week?

16. Practice Write the x & y intercepts. Then GRAPH

17. Practice Write the x & y intercepts. Then GRAPH