Writing Equations of Lines

# Writing Equations of Lines

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## Writing Equations of Lines

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1. Writing Equations of Lines

2. Slope – Intercept Form To write an equation of a line in slope-intercept form, you need … … the y-intercept b … The Slope m Once you have these two things, you can write the equation as y = m x + b DONE

3. Example #1 Write the equation of the line that slope -2 and y-intercept 5. Starting with the slope –intercept form y = m x + b Plug in the slope, and the y –intercept to get y = -2 x + 5 DONE

4. Point – Slope Form To write an equation of a line in point – slope form, all you need is … (x1, y1) … Any Point On The Line … The Slope … m Once you have these two things, you can write the equation as y – y1 = m (x – x1) DONE

5. Example #1 Write the equation of the line that goes through the point (2, –3) and has a slope of 4. Point = (2, –3) Slope = 4 Starting with the point – slope form y – y1 = m (x – x1) Plug in the y-value, the slope, and the x-value to get y + 3 = 4 (x – 2) Notice, that when you subtracted the “–3” it became “+3”. DONE

6. Write the equation of the line that goes through the point (–4, 6) and has a slope of . Point = (–4, 6) Slope = y – 6 = (x + 4) Example #2 Starting with the point – slope form y – y1 = m (x – x1) Plug in the y-value, the slope, and the x-value to get Notice, that when you subtracted the “–4” it became “+4”. DONE

7. Example #3 Write the equation of the line that goes through the points (6, –4) and (2, 8) . We have two points, but we’re missing the slope. Using the formula for slope, we can find the slope to be To use point – slope form, we need a point and a slope. Since we have two points, just pick one … IT DOESN’T MATTER … BOTH answers are acceptable… let’s see why: Using the first point, we have, Using the second point, we have, Point = (6, –4) Slope = –3 Point = (2, 8) Slope = –3 y + 4 = –3 (x – 6) y – 8 = –3 (x – 2) DONE

8. Writing Equations in Slope – Intercept Form y + 4 = –3 (x – 6) y – 8 = –3 (x – 2) Distribute Distribute y + 4= –3x + 18 y – 8 = –3x + 6 Add 8 and combine like terms Subtract 4 and combine like terms y = –3x + 6 + 8 y = –3x + 14 y = –3x + 18 – 4 y = –3x + 14 Notice … They’re the same! DONE

9. 5 4 3 2 1 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 Other Forms of Linear Equations Horizontal Line: y = c , where c is a constant. Example: y = 3 DONE

10. 5 4 3 2 1 -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 Other Forms of Linear Equations Vertical Line: x = c , where c is a constant. Example: x = 2 DONE

11. Write the equation of the line described in slope-intercept form Has slope -5 and y-intercept 3 That contains the point (6, 2) and has slope That contains (-2, -4) and has slope That contains the points (4, 5) and (6, 12) That contains the points (-1, 2) and (5, -4) That is vertical and contains (3, 8) That is horizontal and contains (2, -7) Your turn: DONE