1. FINDING THE SLOPE FROM 2 POINTS Day 91

2. Learning Target: Students can find the slope of a line from 2 given points.

4. Linear equations Linear equations have constant slope (or constant rate of change). For a line on the coordinate plane, slope is the following ratio: vertical change horizontal change change in y change in x = This ratio is often referred to as, or “rise over run,” where rise indicates the number of units moved up or down and run indicates the number of units moved to the left or right. Slope can be positive, negative, zero, or undefined. A line with positive slope goes up from left to right. A line with negative slope goes down from left to right. rise run

6. Zero Slope Undefined Slope Positive Slope Negative Slope

7. If you know any two points on a line, you can find the slope of the line without graphing. The slope of a line through the points (x 1, y 1 ) and (x 2, y 2 ) is as follows: y2 – y1y2 – y1x2 – x1x2 – x1y2 – y1y2 – y1x2 – x1x2 – x1

8. Slope from 2 points Steps: LABEL, WRITE, PLUG AND CHUG!! 1.Label 1.Label points 2.Write 2.Write the slope formula 3.Plug 3.Plug the numbers in the formula 4.Chug 4.Chug out the answers

9. Find the slope of the line that passes through (–2, –3) and (4, 6). Let (x 1, y 1 ) be (–2, –3) and (x 2, y 2 ) be (4, 6). 6 – (–3) 4 – (–2) Substitute 6 for y 2, –3 for y 1, 4 for x 2, and –2 for x 1. 9 6 = The slope of the line that passes through (–2, –3) and (4, 6) is. 3 2 = y 2 – y 1 x 2 – x 1 3 2 =

10. Find the slope of the line that passes through (–4, –6) and (2, -3). Let (x 1, y 1 ) be (–4, –6) and (x 2, y 2 ) be (2, 3). 3 – (–6) 2 – (–4) Substitute 3 for y 2, –6 for y 1, 2 for x 2, and –4 for x 1. 9 6 = The slope of the line that passes through (–4, –6) and (2, 3) is. 3 2 = y 2 – y 1 x 2 – x 1 3 2 =

11. Nonlinear equations have variable rates of change. This means that the rate of change is different between values. This is shown in a graph by a curved line.

12. (LINEAR) (NONLINEAR)

13. (LINEAR)

14. Find the slope of the line passing through each pair of points. 1. (4, 3) and (–1, 1) 2. (–1, 5) and (4, 2) 2 55 3 –

15. Ticket Out The Door Draw and label the different types of slope What is the slope formula? Find the slope from the points (1,7) and (11,12)