1. Standard Form Equation of a Line Name Feb 29, 2011 Are these equations of the SAME LINE? y = x + 2 x – y = -2

2. Standard Form Equation of a Line Name Feb 29, 2011 1. Forms of Equation of a Line: Standard Form 1. You can write the equation of a line in many different ways These equations are still equivalent No matter what form we use, we only need 2 POINTS to graph a line

3. Standard Form Equation of a Line Name Feb 29, 2011 1. Forms of Equation of a Line: Standard Form 1. The Standard Form equation of a line is written: 4x + 2y = 8 How is this different than slope-intercept form? X and y on the same side We don’t easily know m (slope) or b (y-intercept)

4. Standard Form Equation of a Line Name Feb 29, 2011 2. Graphing Standard Form Equation 2. There are 4 steps to graph the Standard Form equation Step 1Draw x/y table with space for two points Step 2Find the y-intercept by setting x=0 and solve for y. First Point (0, y-intercept) Step 3Find the x-intercept by setting y=0 and solve for x Second Point (x-intercept, 0) Step 4Plot Both Points and Draw Line

5. Standard Form Equation of a Line Name Feb 29, 2011 3. Example: Graphing Standard Form 3. Graph: 4x + 2y = 8 Step 1Draw x/y table with space for two points XY

6. Standard Form Equation of a Line Name Feb 29, 2011 3. Example: Graphing Standard Form 3. Graph: 4x + 2y = 8 Step 2Find the y-intercept by setting x=0 and solve for y. First Point (0, y-intercept) 4x + 2y = 8 4(0) + 2y = 8 0 + 2y = 8 2y = 8 y = 4 2 2 First Point (0, 4)

7. Standard Form Equation of a Line Name Feb 29, 2011 3. Example: Graphing Standard Form 3. Graph: 4x + 2y = 8 Step 3Find the x-intercept by setting y=0 and solve for x Second Point (x-intercept, 0) 4x + 2y = 8 4x + 2(0) = 8 4x + 0 = 8 4x = 8 x = 2 4 4 Second Point (2, 0)

8. Standard Form Equation of a Line Name Feb 29, 2011 Step 4 Plot Both Points and Draw Line XY 04 20 3. Example: Graphing Standard Form 3. Graph: 4x + 2y = 8 The y-intercept crosses the y-axis The x-intercept crosses the x-axis WHAT IS THE SLOPE OF THIS LINE?

9. Standard Form Equation of a Line Name Feb 29, 2011 4. Going From Standard Form to Slope- Intercept (y=mx+b) 4. We can go from Standard Form to Slope-Intercept This is useful when you need to calculate slope Using Standard Form equation, find two points: x-intercept and y-intercept (#2 and #3 of these notes)

10. Standard Form Equation of a Line Name Feb 29, 2011 4. Going From Standard Form to Slope- Intercept (y=mx+b) 4. For Slope-Intercept, we need to find two things: Y-Intercept (b): We already have this, the y-coordinate when x=0 (0, b) Slope (m): Use the two points (x- intercept and y-intercept) to calculate slope Then, plug in m and b: y = mx + b

11. Standard Form Equation of a Line Name Feb 29, 2011 5. Example: Going From Standard Form to Slope- Intercept (y=mx+b) 5. Find Slope and Y-Intercept and Write the following equation in Slope-Intercept Form: 4x + 2y = 8 Use the points from #3: XY 04 20

12. Standard Form Equation of a Line Name Feb 29, 2011 5. Example: Going From Standard Form to Slope- Intercept (y=mx+b) 5. Rewrite with values for m and b: y = mx + b y = -2x + 4 Y-Intercept (b): the y-coordinate when x=0 b = 4 Slope (m): use the two points to calculate slope M = (0 – 4) = -4 = -2 (2 – 0) 2 XY 04 20 This is the SAME equation as 4x + 2y = 8