What is Writing an Equation When Given Two Points?

Writing an equation when given two points is a process used in algebra to create an equation from two given points. The equation is written in the form of a line that passes through the two points. This process is useful for creating equations from data points, such as points on a graph. It can also be used to solve for x and y in an equation.

How to Write an Equation When Given Two Points

Writing an equation when given two points is relatively easy. The first step is to get the two points in the form of (x, y). Once you have the points, you can use the slope-intercept form of a line, y=mx+b, to write the equation. The m represents the slope, and the b is the y-intercept. To get the slope, you will need to create a ratio using the two points. The ratio will be (y2-y1)/(x2-x1). This is the slope of the line. To get the y-intercept, you will need to plug the slope into the equation and solve for b.

Example of Writing an Equation When Given Two Points

Consider the points (2,4) and (6,8). To solve for the equation of the line that passes through these two points, you will first need to find the slope. To do this, you will create a ratio using the two points. The ratio is (y2-y1)/(x2-x1). In this case, the ratio is (8-4)/(6-2), which equals 4/4, or 1. Now that you have the slope, you can plug it into the equation, y=mx+b. This equation becomes y=x+b. To solve for b, you will need to plug in one of the points. If you plug in (2,4), the equation becomes 4=2+b. Solving for b gives you b=2. The equation of the line is y=x+2.

Conclusion

Writing an equation when given two points is a useful process for creating equations from data points. It uses the slope-intercept form of a line, y=mx+b, to create the equation. The m represents the slope, and the b is the y-intercept. To get the slope, you will need to create a ratio using the two points. To get the y-intercept, you will need to plug the slope into the equation and solve for b.