Finding Slope of a Line

1. Warm Up Find the slope of the line that passes through each pair of points 1. (3, 6) and (–1, 4) 2. (1, 2) and (6, 1) Course 3 12-3 Using Slopes and Intercepts 4-6 -2 1 -1-3 -4 2 – 1-2 -1 6-1 5

2. Learn to use slopes and intercepts to graph linear equations. Learn to use slopes and intercepts to graph linear equations. Course 3 12-3 Using Slopes and Intercepts

3. Vocabulary Vocabulary x -intercept x -intercept y -intercept y -intercept slope-intercept form slope-intercept form Insert Lesson Title Here Course 3 12-3 Using Slopes and Intercepts

4. 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). Course 3 12-3 Using Slopes and Intercepts

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

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

7. Additional Example 1 Continued The graph of 4 x – 3 y = 12 is the line that crosses the x -axis at the point (3, 0) and the y -axis at the point (0, –4). Course 3 12-3 Using Slopes and Intercepts

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

9. In an equation written in slope-intercept form , y = mx + b , m is the slope and b is the y -intercept. y = m x + b Slope y -intercept Course 3 12-3 Using Slopes and Intercepts

10. Additional Example 2A: Using Slope-Intercept Form to Find Slopes and y -intercepts Write each equation in slope-intercept form, and then find the slope and y -intercept. 2 x + y = 3 –2 x –2 x Subtract 2x from both sides. y = 3 – 2 x Rewrite to match slope-intercept form. y = –2 x + 3 The equation is in slope-intercept form. m = –2 b = 3 The slope of the line 2 x + y = 3 is –2, and the y -intercept is 3. Course 3 12-3 Using Slopes and Intercepts 2 x + y = 3

11. Additional Example 4: Writing Slope-Intercept Form Write the equation of the line that passes through (3, –4) and (–1, 4) in slope-intercept form. Find the slope. The slope is –2. Substitute either point and the slope into the slope- intercept form. y = mx + b 4 = –2 (–1) + b 4 = 2 + b Substitute –1 for x, 4 for y, and –2 for m. Simplify . 4 – (–4) –1 – 3 = y 2 – y 1 x 2 – x 1 8 –4 = = –2 Course 3 12-3 Using Slopes and Intercepts

12. Additional Example 4 Continued Solve for b . Subtract 2 from both sides. Write the equation of the line, using –2 for m and 2 for b . 4 = 2 + b –2 –2 2 = b y = –2 x + 2 Course 3 12-3 Using Slopes and Intercepts

13. Lesson Quiz Write each equation in slope-intercept form, and then find the slope and y-intercept. 1. 2 y – 6 x = –10 Write the equation of the line that passes through each pair of points in slope- intercept form. 3. (0, 2) and (4, –1) y = 3 x – 5; m = 3; b = –5 Insert Lesson Title Here y = – x + 2 3 4 Course 3 12-3 Using Slopes and Intercepts