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Linear equations

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Linear equations

1. 1. February 6, 2008 Linear Equations y = mx + b
2. 2. <ul><li>Slope = rise = m = </li></ul><ul><li>run </li></ul><ul><li>difference of y’s </li></ul><ul><li>difference of x’s </li></ul><ul><li>(3, 2) (4, 7) 7 – 2 = 5 = 5 </li></ul><ul><li>4 – 3 1 </li></ul>
3. 3. <ul><li>y – intercept = b = the point where the line crosses the y axis = starting point when graphing </li></ul><ul><li>b = -6 </li></ul>
4. 4. <ul><li>Special lines only contain one variable: </li></ul><ul><li>x = any number ( vertical line ) </li></ul><ul><li>Slope: Undefined </li></ul><ul><li>x = 7 </li></ul><ul><li>y = any number ( horizontal line ) </li></ul><ul><li>Slope : Zero </li></ul><ul><li>y = 7 </li></ul>
5. 5. <ul><li>Finding the equation of the line in y= mx + b form. Given: Two points. First find the slope (m) and then substitute one of the points x and y values into point-slope form </li></ul><ul><li>(y – y 1 = m(x – x 1 ) along with the slope. Simplify. </li></ul>
6. 6. <ul><li>Finding the equation of the line in y = mx + b form. Given: slope (m) and a point (x,y). Substitute x, y, and m into point-slope form and simplify. (y – y 1 = m(x – x 1 ) </li></ul>
7. 7. <ul><li>Finding the equation of the line in y= mx + b form. Given: slope and y-intercept. Substitute the “m” with the slope value and the “b” with the y-intercept value. </li></ul><ul><li>Slope: 5 y-intercept: -2 </li></ul><ul><li>Equation: y = 5x - 2 </li></ul>
8. 8. <ul><li>Graphing the line – start with the </li></ul><ul><li>y-intercept and then move the rise and then the run. Positive slopes increase from left to right. Negative slopes decrease from left to right </li></ul>