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# Writing linear equations

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### Writing linear equations

1. 1. Writing Linear Equations <ul><li>Using Slope Intercept Form </li></ul><ul><li>Point-Slope Form. </li></ul>
2. 3. <ul><li>We’ve learned to graph given an equation. </li></ul><ul><li>Now we’ll learn to write the equation given the graph </li></ul><ul><li>There are three ways. </li></ul><ul><li>It all depends on what information you are given as to which process you use. </li></ul>
3. 4. Slope-Intercept Form <ul><li>y = mx + b [or f ( x ) = mx + b ] </li></ul><ul><li>m is the slope </li></ul><ul><li>b is the y -intercept </li></ul>
4. 5. Find the Equation of the Line <ul><li>What is the </li></ul><ul><li>y -intercept? </li></ul><ul><li>b = -2 </li></ul><ul><li>What is m ? </li></ul><ul><li>m = </li></ul><ul><li>y = x -2 </li></ul>x y
5. 6. Find the Equation of the Line <ul><li>b = ? </li></ul><ul><li>b = 1 </li></ul><ul><li>m = ? </li></ul><ul><li>m = - </li></ul><ul><li>y = - x + 1 </li></ul>x y
6. 7. Find the Equation of the Line <ul><li>b = ? </li></ul><ul><li>b = 4 </li></ul><ul><li>m = ? </li></ul><ul><li>m = 0 </li></ul><ul><li>y = 0 x + 4 </li></ul><ul><li>y =4 </li></ul>x y
7. 8. Find the Slope and y-intercept of each Equation: <ul><li>1) y = -4 x + 3 </li></ul><ul><li>m = -4 </li></ul><ul><li>b = 3 </li></ul><ul><li>2) y = 5 - x </li></ul><ul><li>m = - </li></ul><ul><li>b = 5 </li></ul><ul><li>3) 8 x + y = </li></ul><ul><li>m = -8 </li></ul><ul><li>b = </li></ul><ul><li>4) 4 x - 2 y = 10 </li></ul><ul><li>m = 2 </li></ul><ul><li>b = -5 </li></ul>
8. 9. Find the Equation Given the Slope and y -intercept <ul><li>1) m = -3, b = 1 </li></ul><ul><li>y = -3 x + 1 </li></ul><ul><li>2) m = - , b = -4 </li></ul><ul><li>y = - x - 4 </li></ul>
9. 10. Find the Equation Given the Slope and a Point <ul><li>Given m = -1, (2, 1) </li></ul><ul><li>First, calculate b by substituting the slope and the coordinates into y = mx + b. </li></ul><ul><li>y = -1 x + b </li></ul><ul><li>1 = -1(2) + b </li></ul><ul><li>1 = -2 + b </li></ul><ul><li>3 = b </li></ul><ul><li>y = -1 x + 3 </li></ul>
10. 11. If you are given two points on the line <ul><li>Find the slope using the two points </li></ul><ul><li>Then plug this slope and either one of the points into the point slope formula. </li></ul>
11. 12. Find the Equation Given Two Points <ul><li>Given (-1, 3) and (2, 1) </li></ul><ul><li>First, calculate the slope: </li></ul><ul><li> Second, find b . Use either point... </li></ul><ul><li>m = , (2, 1) </li></ul><ul><li>1 = (2) + b </li></ul><ul><li>1 = + b </li></ul><ul><li> </li></ul><ul><li> = b </li></ul>
12. 13. Use Point Slope Form: If you are given slope, m, and a point (x 1 ,y 1 ) on the line <ul><li>y – y 1 = m ( x – x 1 ) </li></ul>
13. 14. Write an equation of a line containing the point (1,2) with slope of -1/2. <ul><li>Use (x 1 ,y 1 ) = (1,2) & m = -1/2 </li></ul><ul><li>y – 2 = -1/2 ( x – 1) </li></ul><ul><li>Now you can simplify to the slope intercept form </li></ul><ul><li>y – 2 = -1/2 x + ½ </li></ul><ul><li>y = -1/2 x + 5/2 </li></ul>
14. 15. Given two points (-2,2) & (3,7) <ul><li>Find the slope: </li></ul><ul><li>m=1 </li></ul><ul><li>Plug this slope and one of the points into the point slope formula. </li></ul><ul><li>y – 2 = 1 ( x – (-2)) </li></ul><ul><li>y – 2 = x + 2 </li></ul><ul><li>y = x + 4 (put the equation into slope intercept form) </li></ul>(-2,2) (3,7)