1. Remember slope is a rate of change so it is the difference of the y coordinates over the difference of the x coordinates. Precalculus Functions & Graphs Notes Slope of a Line 2.3 Lines A horizontal line has zero slope. A vertical line has no slope or undefined slope.

2. To sketch the line plot points A and B and draw the line between them. Precalculus Functions & Graphs Example #1 Sketch the line through A and B, and find its slope m. 2.3 Lines Now find the slope using the slope formula.

3. Precalculus Functions & Graphs You Try #1 Find the slope of the line through points A and B. 2.3 Lines Answer choices will appear after you have had time to try the problem.

4. To sketch the first line plot P. Precalculus Functions & Graphs Example #2 Sketch the graph of the line through P for each value of m. 2.3 Lines Now for the first line go up 2 and right 3 and draw line. For the 2 nd line go down 3 and right 1 from P and draw line. For the 3 rd line go down 1 and right 4 from P and draw line.

5. Where m is the slope and b is the y-intercept. Precalculus Functions & Graphs Notes Slope-intercept form of a line 2.3 Lines Remember to graph a line using slope intercept you plot the intercept first and then from the intercept you “do” the slope; always run right!!!!

6. Remember for the 1 st b is 1 and m is -3. So from b go down 3 and right 1. Precalculus Functions & Graphs Example #3 Sketch the graphs of the lines on the same coordinate plane. 2.3 Lines For the 2 nd b is -2 and m is -3. So from b go down 3 and right 1. What do you notice about these lines? For the 3 rd line b is 1 and m is 1/3 so from b go up 1 and right 3. What do you notice? Parallel! Perpendicular!

7. Perpendicular lines have slopes that are negative reciprocals of each other. Precalculus Functions & Graphs Notes Parallel lines have equal slopes 2.3 Lines In the previous example the slope of the green and red lines were both -3. They were parallel and the slopes were equal. The slope of the purple line was 1/3 and -3 x 1/3 = -1. The slopes are negative reciprocals so they are perpendicular.

8. We use this to find the equation of a line when we have a point on the line and the slope of the line. Precalculus Functions & Graphs Notes Point-Slope Form of a Line. 2.3 Lines General or Standard Form of a Line. Where a is non-negative, and a, b, and c are relatively prime integers (a, b, and c have no common factors).

9. Using point-slope, replace m with -4 and x 1 with -2, and y 1 with 3. Precalculus Functions & Graphs Example #4 Using Point-Slope Find a general form of an equation of the line through the point A that satisfies the given condition. 2.3 Lines Now convert to standard or general form.

10. Using slope-intercept replace m with -4 and x with -2, and y with 3 to find b. Precalculus Functions & Graphs Example #4 Using Slope-Intercept Find a general form of an equation of the line through the point A that satisfies the given condition. 2.3 Lines Now replace m and b in slope-intercept. Put in standard or general form.

11. First use the slope formula to find the slope. Precalculus Functions & Graphs Example #5 Find a general form of an equation of the line through the point A that satisfies the given condition. 2.3 Lines Then use either point-slope or slope intercept and one of the points to find the equation in standard form.

12. First use the slope formula to find the slope. We already found the slope in example 5. Precalculus Functions & Graphs Example #6 Find a general form of an equation for the perpendicular bisector of the segment AB. 2.3 Lines Then find the midpoint of AB. Now find the equation using the new slope and the midpoint.

13. Precalculus Functions & Graphs You Try #2 Find a general form of an equation of the line through the point A that satisfies the given condition. 2.3 Lines Answer choices will appear after you have had time to try the problem.

14. Precalculus Functions & Graphs You Try #3 Find a general form of an equation of the line through the point A that satisfies the given condition. 2.3 Lines

15. Answer choices will appear after you have had time to try the problem. Precalculus Functions & Graphs You Try #4 Find the slope-intercept form of the line that satisfies the given conditions. 2.3 Lines