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.
2. Suppose you were shown this graph: Graph from purplemath.com How would you find the equation of this line?
3. The basic equation for a straight line is: Y=mx+b where m=the slope and b=the y-intercept.
4. Slope Slope is determined by Δy/Δx RISE OVER RUN When using a graph, count the number of boxes up or down, and then across from point to point. Run(ΔX) =3 Rise(ΔY) =2 Graph from purplemath.com
5. Slope If you don’t have a graph, the slope of the graph is obtained by: (Y2-Y1) (X2-X1) You will be using 2 coordinate points. Any points on the line are acceptable.
6. For Example: Find the slope of a line which contains these 2 points: (2, 4) and (3, 5) {(x1, y1) and (x2, y2)} (5-4)/(3-2) = 1/1 = 1
7. Visually Identifying Positive and Negative Slope Graphs from purplemath.com Positive Slope (2/3) Because from left to right, the line is increasing. Negative Slope (-2) Because from left to right, the line is decreasing.
8. No Slope and Undefined Slope Graphs from purplemath.com Undefined Slope: This means all of the x values are the same. For example your slope might be -2/0, which is undefined. No Slope: This means all of the y values are the same. For example, your slope might be 0/2, which is just 0.
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. Graph from purplemath.com
10. Remember: Y=mx+b 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. You will plug in 3 for the x, -2 for the y, and 2/3 for m. -2= (2/3)(3)+b -2=2+b -4=b
11. Therefore, the equation of that graph is: Y=2/3x+b This is considered slope intercept form. There is also Point Slope Form: Y-Y1=m(X-X1) 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.
12. Using Point Slope form, we will determine the equation of a straight line with a slope of 2, containing the point (3, 4). Y-4=2(X-3) Y-4=2X-6 Y=2X-2 Therefore, the line crosses the Y-axis at (0,-2)
13. Sources: Stapel, Elizabeth. "Slope of a Straight Line." Purplemath. Last updated 2010. Accessed 27 February 2010 Available from: http://www.purplemath.com/modules/slope.htm Spears, Shane. “Algebra: Rise Over Run Made Easy.” Suite101. Written 15 December 2009. Accessed 28 February 2010. Available from: http://curriculalessons.suite101.com/article.cfm/rise_over_run_made_easy
