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# 1.4 equations

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### 1.4 equations

1. 1. 1.4 Equations/Formulas
2. 2. Linear Equations • Equations are like recipes! • They tell us how to make a picture (graph) of a function •We just have to know how to read the recipe…
3. 3. Slope-Intercept Form (S-IF) • y = mx + b • b is the y-intercept. ▫ Tells us where to begin. • m is the slope. ▫ Tells us how to move.
4. 4. Graphing from S-IF • Plot y-intercept first (on the Y-AXIS!!) • Use the slope to plot more points. ▫ Remember: Slope is rise ! run Example: y = 2x – 4
5. 5. Example: • Graph
6. 6. You Try! • Graph y = -3x + 6
7. 7. Writing Equations from Graphs • In slope-intercept form: • Find the y-intercept ▫ This is b! • Count the slope and reduce ▫ This is m! •Write equation ▫ Leave x and y, just replace m and b!
8. 8. Example: •Write an equation in S-IF for the graph shown. (Draw in the points first!) • y = ____ x + ____
9. 9. Example: •Write an equation in S-IF for the graph shown.
10. 10. You Try! •Write an equation in S-IF for the graph shown.
11. 11. Point-Slope Form (P-SF) • y = m(x – x1) + y1 •m is still slope • x1 and y1 are coordinates of a point (x1, y1) on the line
12. 12. Graphing from P-SF 1. Write the ordered pair for your point (x1, y1) ▫ Need to change the sign of the x-coordinate since it’s y = m(x – x1) + y1 ▫ For example, the point for y = 2(x + 3) – 1 is (-3, -1). 2. Plot that point. 3. From there, use the slope (m) to plot more points
13. 13. Example: • Graph y = (x + 4) + 3
14. 14. Example: • Graph y = 4(x – 3) + 5
15. 15. You Try! • Graph y = -(x + 2) – 4
16. 16. Writing Equations from Graphs • In point-slope form: • Find ANY point on the line ▫ This is (x1, y1)! • Count the slope and reduce ▫ This is m! •Write equation y = m(x – x1) + y1 ▫ Leave x and y, just replace m, x1 and y1!
17. 17. Example: •Write an equation in P-SF for the graph shown. y = ___(x - ___) +___
18. 18. Example: •Write an equation in P-SF for the graph shown.
19. 19. You Try! •Write an equation in P-SF for the graph shown.