There are several forms that the equation of a line can take. They may look different, but they all describe the same line--a line can be described by many equations. All (linear) equations describing a particular line, however, are equivalent.
The first of the forms for a linear equation is slope-intercept form. Equations in slope-intercept form look like this:
|y = mx + b|
To write an equation in slope-intercept form, given a graph of that equation, pick two points on the line and use them to find the slope. This is the value of m in the equation. Next, find the coordinates of the y -intercept--this should be of the form (0, b) . The y - coordinate is the value of b in the equation.
Finally, write the equation, substituting numerical values in for m and b . Check your equation by picking a point on the line (not the y -intercept) and plugging it in to see if it satisfies the equation.
Example 1: Write an equation of the following line in slope-intercept form:
Example 2: Write an equation of the line with slope m = which crosses the y -axis at (0, - ) .
y = x -
Example 3: Write an equation of the line with y -intercept 3 that is parallel to the line y = 7x - 9 .
Since y = 7x - 9 is in slope-intercept form, its slope is 7 .
Since parallel lines have the same slope, the slope of the new line will also be 7 . m = 7 . b = 3 .
Thus, the equation of the line is y = 7x + 3 .
Example 4: Write an equation of the line with y -intercept 4 that is perpendicular to the line 3y - x = 9 .
The slope of 3y - x = 9 is .
Since the slopes of perpendicular lines are opposite reciprocals, m = - 3 . b = 4 .
Thus, the equation of the line is y = - 3x + 4 .