Equations in point slope form are equations used to express the relationship between two points on a line. This type of equation is useful when you need to calculate the slope or the y-intercept of a line. It is also used in many applications in mathematics, science, engineering, and other fields. To write equations in point slope form, there are four steps that need to be followed.

## Step 1: Identify the Slope

The first step in writing equations in point slope form is to identify the slope. The slope of a line is the change in its y-value divided by the change in its x-value. It is often represented by the letter m. To find the slope, you will need two points on the line. Once you have the two points, you can calculate the slope using the formula: m = (y2 – y1) / (x2 – x1).

## Step 2: Find the Y-Intercept

The next step is to find the y-intercept. The y-intercept is the point at which the line crosses the y-axis. To find the y-intercept, you need to plug in the x-value of one of the points on the line into the equation. The y-intercept is the value of y at that point. Once you have the y-intercept, you can move on to the next step.

## Step 3: Write the Equation

Now that you have the slope and the y-intercept, you can write the equation in point slope form. The equation in point slope form looks like this: y – y1 = m(x – x1). The terms y1 and x1 represent the coordinates of the point you used to calculate the slope and y-intercept. The m represents the slope of the line. Once you have the equation written, you are ready to move on to the fourth step.

## Step 4: Graph the Equation

The last step is to graph the equation. This can be done using a graphing calculator or a graphing program. To graph the equation, you need to plot the coordinates of the two points that you used to calculate the slope and the y-intercept. Then draw a line connecting the two points. This line should be the same line that your equation represents. If it is not, then you have made a mistake in calculating the slope or y-intercept.

Writing equations in point slope form is an important skill to have in mathematics, science, engineering, and other fields. It is a useful tool for finding the slope and the y-intercept of a line. The process of writing equations in point slope form involves four steps: identifying the slope, finding the y-intercept, writing the equation, and graphing the equation. Following these steps will help you write equations in point slope form correctly and accurately.