Week 2-Straight Lines and Associated Equations

One of the primary equations associated with straight lines is the slope-intercept equation. To understand how to use this equation, one must understand the equation. The slope-intercept equation or y = mx + b, has coordinates (x,y) as points on the line, m as the slope of the line, and b, as the y coordinate (0,y) on the line that crosses the y-axis when the x = 0 (the y intercept). Slope (m) is defined as the change in y divided by the change in x.

If you have an equation, y = 2x+ 3, then m=2, b=3, and two points on the line are (0,3) or (1,5). Notice that there are many solutions to this equation. For any given x value, a y value can be calculated. The slope or m is then calculated by subtracting the y values or 5-3= 2, subtracting the x values or 1- 0=1 and then dividing the y by the x or y/x = 2/1 or 2.

Any equation that has these same elements can be converted into an equation to find the slope, y intercept or a point (x,y) on the line. You just need to have at least two of these values. What you need to do is to move the elements of the equation around until it fits into the basic  y = mx + b format. Take the equation -2x + y = 3. If you add 2x to both sides of the equation, the equations would read, -2x +2x + y = 3 + 2x or y = 2x + 3.

I didn't include a 2-dimensional picture of this line, but it can be easily drawn.

I hope this helps.

Ken

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