2. 1.2 Slopes and Intercepts Objectives: Graph a linear equation. Write a linear equation for a given line in the coordinate plane. Standards: 2.8.11.K Apply an appropriate technique to graph a linear function. 2.8.11.L Write the equation of a line when given the graph of the line.

3. I. Write the equation in slope-intercept form for the line that has the indicated slope, m, and y-intercept, b. m = 3, b = -2 y = 3x - 2 m = ½, b = ¾ y = 1/2x + 3/4 m = 0, b = 5 y = 5 m = -2, b = 0 y = -2x

4. II. Identify the slope, m, and y-intercept, b, for each line. Then graph.  Positive slope goes up to the right & negative slope goes down to the right. y = x + 3 * m = _______ b = _______ x + y = 6 * m = _______ b = _______

5. II. Identify the slope, m, and y-intercept, b, for each line. Then graph. 3x + 6y = 18 * m = ________ b = ________

6. III. Find the slope of a line if you know the coordinates of two points on the line. In a graph, the slope of a line is the change in vertical units divided by the corresponding change in the horizontal units. m = Change in y = Rise = y 2 – y 1 Change in x Run x 2 – x 1 (0, 4) and (3, 1)

7. m = Change in y = Rise = y 2 – y 1 Change in x Run x 2 – x 1 (1, -3) and (3, -5) (3, -2) and (4, 5) (-10, -4) and (-3, -3)

8. IV. Find the x and y intercepts. The x intercept of a graph is the x-coordinate of the point where the graph crosses the x-axis. In order to find the x intercept (x, 0), substitute zero for y in an equation for the line and solve for x. The y intercept of a graph is the y-coordinate of the point where the graph crosses the y-axis. In order to find the y intercept (0, y), substitute zero for x in an equation for the line and solve for y.

9. IV. Find the x and y intercepts. 4x + y = -4 x-intercept y-intercept x + ½ y = -2 x-intercept y-intercept

10. IV. Find the x and y intercepts. 1. x + 3y = 12 2. -3x + y = -9 3. x – y = -14. 5x – 8y = 16 5. 7x + 3y = 26. -x + 8y = -6

11. V. Vertical Lines vs. Horizontal Lines A horizontal line is a line that has a slope of zero. y = # is a horizontal line. A vertical line is a line that has an undefined slope. x = # is a vertical line. x = -2Vertical Line Undefined Slope y = 2Horizontal Line Zero Slope y = 9 Horizontal Line Zero Slope

12. VI. Write an equation in slope intercept form for each line. Ex 1. A line passing through (2, 4) with a slope of ½. Ex 2. A line with a slope of zero passing through (-2, -6). Zero slope means it’s a horizontal line so y = #

13. VI. Write an equation in slope intercept form for each line. Ex 3. A line passing through (0, -1) and (2,2).

14. Writing Activities: Slopes and Intercepts 1a). In your own words, define the slope of a line. 1b). Give an example of three lines with the same slope.

15. Writing Activities: Slopes and Intercepts 2a). In your own words, define the y- intercept of a line. 2b). Give an example of three lines with the same y-intercept.

16. Writing Activities: Slopes and Intercepts 3). What are the characteristics of a line that has the equation y = mx? 4). What does the slope of a line indicate about the line? Include some examples. 5). Explain the difference between a line with a slope of 0 and a line with no slope.

18. Homework Integrated Algebra II- Section 1.2 Level A Honors Algebra II- Section 1.2 Level B