On this page, we hope to clear up problems that you might
have with finding the equation of a line.
Many times, you'll have the graph of an equation shown to you and you'll need to find the equation. This seems a very daunting task, but it's actually quite easy!
For example, take a horizontal line such as y = 2. Every point on that graph is 2 units above the x axis. All horizontal lines have equations that are written in the same format, such as y = -4.5. Because they're all written the same way, we can come up with a general formula for horizontal lines. It is the following equation (where k represents any real number): y = k. Under the same assumptions, the general formula for vertical lines can be written as follows (where k represents any real number): x = k.
Linear equations such as y = .009x + 34 also have a general equation that can represent any linear equation. It is written as follows: y = mx + b.
The things to remember about the above formula, which is called the slope-intercept formula, are outlined below.
1. Since you know a line with an equation in that form cannot be horizontal or vertical, all you need to find are m and b to find the equation.
2. b is called the intercept. It is the point when the line crosses the y axis.
3. m is called the slope. The slope has both a sign (either + or -) and a value (the number behind the sign). For example, the equation y = -3x + 4 has a negative sign and a value of three. Therefore, the slope is -3. When looking at a graph, you can always tell if the slope is negative or positive by the direction it points. When looking for the sign of a slope, look at the left side of the graph. Then, look at the right side of the graph. If the right side is lower than the left side, the line has a negative slope, if the right side is higher, the line has a positive slope.
To find the value of the slope, you compute the rise over the run To do that, pick two points on the line at random and then draw a line through each of those points that run parallel to the coordinate axes. Count the number of units between the point on the line and where the two addition lines you drew intersect. The number of units on the horizontal line is the run and the number of units on the vertical line is the rise. Dividing the rise by the run gives you the value of the slope.
1. Find the equation of the line graphed in the accompanying figure:
Solution: The desired equation is in the slope-intercept form. You need to find m and b.
Back to Graphing on the Coordinate Plane.