Question 250727
If you have two points on the line, then just plot them and draw a line through them. Otherwise...<ol><li>Find a point on the line. Any point will work but some are better than others. (If (-143, 2035) is a point on the line it will not be convenient to use it.) Often the y-intercept is used. Just pick a value for x and use that value and the equation to find the y for that x.</li><li>Plot the point on the graph.</li><li>Find the slope of the line. There are several common ways of finding the slope of a line:<ul><li>If the equation is in (or has been transformed into) slope-intercept form, y = mx + b, the slope is the coefficient of x. (Note: This form is also useful for finding the y-intercept which can be used for the point in steps #1 and #2.)</li><li>If the equation is in (or has been transformed into) Standard form, Ax + By = c, then the slope is -A/B.</li><li>Find a second point on the line and use the slope formula: {{{m = (y[2] - y[1])/(x[2] - x[1])}}}</li></ul></li><li>If the slope is not a fraction, write it as a fraction. Any fraction equal to the slope will work. For example, if the slope is 2 we could use any of these: 2/1, 4/2, 6/3, -2/-1, etc.</li><li>Starting from the point you graphed at step #2:<ul><li>go up or down based on the numerator of the slope</li><li>go right or left based on the denominator of the slope</li><li> and plot a point where you end up.</li></ul></li><li>Use a ruler and draw a line through the two points.</li></ol>
Here's a simple example: To graph the equation y = -3x + 1...
1) Find a point on the line. Since this equation is in slope-intercept form we can simply "read" the y-intercept of 1.
2) Plot the point. Plot a point at 1 on the y-axis: (0, 1)
3) Find the slope. We can also "read" the slope from the slope-intercept form: -3.
4) Write the slope as a fraction. We can use -3/1.
5) Starting from our plotted point (0, 1) we go down 3 (because the numerator of the slope is -3) and to the right by 1 (because the denominator of the slope fraction is 1). This should put us at (1, -2). Plot this point.
6) Draw a line through the two points (0, 1) and (1, -2)<br>
If we use 3/-1 for the slope fraction instead of -3/1, we end up with the same line, believe it or not. We start from (0, 1) and go up 3 (because the numerator of the alternate slope fraction is 3) and go to the left by 1 (because the denominator of the alternate slope fraction is -1). This puts us at (-1, 4). Even though the two points we use are different, when we draw a line through each pair, we end up with the same line!