(0 2) And (3 3) In Slope Intercept Form

3 min read Jul 03, 2024

Understanding Slope-Intercept Form: (0, 2) and (3, 3)

The slope-intercept form is a fundamental concept in algebra and is used to express linear equations. In this article, we will explore how to write the slope-intercept form of a line using two points: (0, 2) and (3, 3).

What is Slope-Intercept Form?

The slope-intercept form is a way of expressing a linear equation in the form of y = mx + b, where:

m is the slope of the line (a measure of how steep it is)
b is the y-intercept (the point at which the line crosses the y-axis)

Finding the Slope-Intercept Form using (0, 2) and (3, 3)

To find the slope-intercept form of a line using two points, we need to find the slope (m) and the y-intercept (b).

Step 1: Find the Slope (m)

The slope (m) can be found using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (0, 2) and (x2, y2) = (3, 3)

m = (3 - 2) / (3 - 0) m = 1 / 3 m = 1/3

Step 2: Find the Y-Intercept (b)

To find the y-intercept (b), we can use one of the points and the slope (m). Let's use the point (0, 2).

y = mx + b 2 = (1/3)(0) + b 2 = b

So, the y-intercept (b) is 2.

Step 3: Write the Slope-Intercept Form

Now that we have the slope (m) and the y-intercept (b), we can write the slope-intercept form of the line:

y = mx + b y = (1/3)x + 2

And that's it! We have successfully found the slope-intercept form of the line using the points (0, 2) and (3, 3).

Recap

In this article, we learned how to find the slope-intercept form of a line using two points: (0, 2) and (3, 3). We found the slope (m) to be 1/3 and the y-intercept (b) to be 2, resulting in the slope-intercept form:

y = (1/3)x + 2