As we have seen before, you can write the equation of any line in the form of y = mx + b . This is the so-called slope intercept form, because it gives you two important pieces of information: the slope m and the y-intercept b of the line. You can use these values for linear interpolation later
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
where m is the slope of the line and b is the y-intercept of the line, or the y-coordinate of the point at which the line crosses the y-axis.
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.
Step-by-step explanation:
Example: 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.
