The Slope-Intercept Formula

In geometry, the slope-intercept formula is a way to find the equation of a line when given certain information. The formula is written as y = mx + b, where m is the slope and b is the y-intercept. In this blog post, we'll break down what each of these terms means and how to use the formula.

The slope of a line is a measure of how steep it is. It's calculated by finding the ratio of rise over run—that is, the difference in y-values divided by the difference in x-values. For example, consider the line shown in Figure 1.

Figure 1

To find the slope, we would take any two points on the line and calculate the rise over run. Let's choose the points (2, 3) and (4, 5). The rise is the difference in y-values, which is 3 - 5 = -2. The run is the difference in x-values, which is 4 - 2 = 2. So, our slope is -2/2 = -1.

Now that we know how to calculate slope, let's talk about what a y-intercept is. The y-intercept is simply the point where a line intersects with the y-axis. In other words, it's the value of y when x = 0. If we look back at Figure 1, we can see that when x = 0, y = 2. Therefore, our y-intercept for this line is 2.

With this information, we can now fill in our formula: y = mx + b. In our example, m = -1 and b = 2. So, our equation becomes y = -1x + 2. And that's all there is to it! Now you know how to use the slope-intercept formula to find equations for lines in geometry.

The slope-intercept formula is a quick and easy way to find equations for lines in geometry. All you need are two points on the line and a little bit of algebraic know-how. With this tool in your geometry toolkit, you'll be able to solve problems with ease. Thanks for reading!