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# Finding The Equation of a Straight Line

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This power point is intended for upper level middle school students, and lower level high school students. It explains finding the equation of a line using graphical and algebraic methods, including point slope form and y-intercept form.

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### Finding The Equation of a Straight Line

1. 1. Finding the Equation of a Straight Line<br />Ms. Miloch’s Algebra Class<br />
2. 2. Suppose you were shown this graph:<br />Graph from purplemath.com<br />How would you find the equation of this line?<br />
3. 3. The basic equation for a straight line is: <br />Y=mx+b<br />where <br />m=the slope <br />and b=the y-intercept.<br />
4. 4. Slope<br />Slope is determined by Δy/Δx<br />RISE OVER RUN<br />When using a graph, count the number of boxes up or down, and then across from point to point.<br />Run(ΔX) <br />=3<br />Rise(ΔY)<br />=2<br />Graph from purplemath.com<br />
5. 5. Slope<br />If you don’t have a graph, the slope of the graph is obtained by: <br />(Y2-Y1)<br />(X2-X1)<br />You will be using 2 coordinate points. Any points on the line are acceptable. <br />
6. 6. For Example:<br />Find the slope of a line which contains these 2 points: <br />(2, 4) and (3, 5)<br /> {(x1, y1) and (x2, y2)}<br />(5-4)/(3-2) = 1/1 = 1<br />
7. 7. Visually Identifying Positive and Negative Slope<br />Graphs from purplemath.com<br />Positive Slope (2/3)<br />Because from left to right, the line is increasing. <br />Negative Slope (-2)<br />Because from left to right, the line is decreasing.<br />
8. 8. No Slope and Undefined Slope<br />Graphs from purplemath.com<br />Undefined Slope:<br />This means all of the x values are the same. For example your slope might be -2/0, which is undefined.<br />No Slope: <br />This means all of the y values are the same. For example, your slope might be 0/2, which is just 0.<br />
9. 9. Once you obtain the slope of a line, you need to determine the “b” of the equation, or the y-intercept. On a graph, this is determined my locating where the line crosses the y-axis.<br />Graph from purplemath.com<br />
10. 10. Remember: Y=mx+b<br />In order to find the y-intercept without a graph, you need this equation and a coordinate point from the graph. For example, the graph in the previous slide contains the point (3, -2) and has a slope of 2/3. <br />You will plug in 3 for the x, -2 for the y, and 2/3 for m. <br />-2= (2/3)(3)+b<br />-2=2+b<br />-4=b<br />
11. 11. Therefore, the equation of that graph is:<br />Y=2/3x+b<br />This is considered slope intercept form. There is also <br />Point Slope Form:<br />Y-Y1=m(X-X1) <br />With this form, you also need a coordinate point, which you plug in for Y1 and X1. And you also need the slope. This form is another method used for determining the y-intercept.<br />
12. 12. Using Point Slope form, we will determine the equation of a straight line with a slope of 2, containing the point (3, 4).<br />Y-4=2(X-3)<br />Y-4=2X-6<br />Y=2X-2<br />Therefore, the line crosses the Y-axis at (0,-2)<br />
13. 13. Sources:<br />Stapel, Elizabeth. "Slope of a Straight Line." Purplemath. Last updated 2010. Accessed 27 February 2010 Available from:<br />http://www.purplemath.com/modules/slope.htm<br />Spears, Shane. “Algebra: Rise Over Run Made Easy.” Suite101. Written 15 December 2009. Accessed 28 February 2010. Available from:<br />http://curriculalessons.suite101.com/article.cfm/rise_over_run_made_easy <br />