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Module 4 topic 3 similar problems

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Writing Linear Functions

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Module 4 topic 3 similar problems

1. 1. Module 4 Topic 3<br />Writing Equations of Linear Functions<br />
2. 2. Example 1<br />Similar Problem: What is the equation in slope-intercept form of the following?<br />Let's pretend that the x-intercept is 3 so the ordered pair would be (3, 0) and the other ordered pair is (1, 1).<br />1) Find the slope.<br />(3, 0) and (1, 1)<br />m = (1 - 0)/(1 - 3) = 1/-2<br />m = -1/2<br />2) Use the slope and either point to plug into point-slope form, let's use (1, 1)<br />y - y = m(x - x)<br />y - 1 = -1/2(x - 1)<br />y - 1 = -1/2 x + 1/2<br />y = -1/2 x + 3/2<br />
3. 3. Example 2<br />Similar Problem: What is the equation of the following line?<br />Anytime there is a horizontal line the equation of the line is always going to be y = y. If you were to take the ordered pairs off of the line given you would have (2, 3), (5, 3), (4, 3), (-2, 3), etc.<br />So the equation of the line is y = 3.<br />
4. 4. Example 3<br />Similar Problem: What is the equation of the following line?<br />Anytime there is a vertical line the equation of the line is always going to be x = x. If you were to take the ordered pairs off of the line given you would have (2, 0), (2, 1), (2, 2), (2, 3), etc.<br />So the equation of the line is x = 2. <br />
5. 5. Example 4<br />Similar Problem: Write an equation in slope-intercept form of the line that passes through the point (-5, 2) and has a slope of -5/4.<br />Use the point and the slope and plug into point-slope form.<br />Solve for y.<br />y - y = m(x - x)<br />y - 2 =-5/4 (x - -5)<br />y - 2 = -5/4 (x + 5)<br />y - 2 = -5/4 x + -25/4<br />y = -5/4 x - 17/4<br />
6. 6. Example 5<br /> Similar Problem: What is the equation in slope-intercept form of the line through the points (3, -1) and (-2, 9)?<br />1) Find the slope.<br />m = (9 - -1)/(-2 - 3)<br />m = 10/-5 = -2<br />2) Use the slope and either point to plug into point slope form, let's use (3, -1)<br />y - y = m(x - x)<br />y - -1 = -2(x - 3)<br />y + 1 = -2(x - 3)<br />y + 1 = -2x + 6<br />y = -2x - 5<br />
7. 7. Example 6<br />Similar Problem: Write the equation in slope-intercept form: 6x - 4y = 24.<br />6x - 4y = 24 (solve for y.)<br />Subtract 6x to both sides.<br />-4y = -6x + 24<br />Divide each side by -4.<br />y = 3/2 x - 6<br />
8. 8. Example 7<br />Similar Problem: Write the equation in slope-intercept form: 6x - 4y = 24.<br />6x - 4y = 24 (solve for y.)<br />Subtract 6x to both sides.<br />-4y = -6x + 24<br />Divide each side by -4.<br />y = 3/2 x - 6<br />
9. 9. Example 8<br />Similar Problem: What is the equation in slope-intercept form of the line through the points (3, -1) and (-2, 9)?<br />1) Find the slope.<br />m = (9 - -1)/(-2 - 3)<br />m = 10/-5 = -2<br />2) Use the slope and either point to plug into point slope form, let's use (3, -1)<br />y - y = m(x - x)<br />y - -1 = -2(x - 3)<br />y + 1 = -2(x - 3)<br />y + 1 = -2x + 6<br />y = -2x - 5<br />
10. 10. Example 9 <br />Similar Problem: What is the equation in slope-intercept form of the line through the points (3, -1) and (-2, 9)?<br />1) Find the slope.<br />m = (9 - -1)/(-2 - 3)<br />m = 10/-5 = -2<br />2) Use the slope and either point to plug into point slope form, let's use (3, -1)<br />y - y = m(x - x)<br />y - -1 = -2(x - 3)<br />y + 1 = -2(x - 3)<br />y + 1 = -2x + 6<br />y = -2x - 5<br />