(4 5) In Slope Intercept Form

4 min read Jul 03, 2024

Representing a Line in Slope-Intercept Form: (4, 5)

In algebra, slope-intercept form is a way to express a linear equation in the form of y = mx + b, where m represents the slope of the line and b represents the y-intercept. In this article, we will explore how to represent a line that passes through the point (4, 5) in slope-intercept form.

Understanding the Slope-Intercept Form

Before we dive into the problem, let's review the slope-intercept form. The general equation of a line in slope-intercept form is:

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 where the line crosses the y-axis)

Finding the Slope-Intercept Form of the Line

To find the slope-intercept form of the line that passes through the point (4, 5), we need to find the slope m and the y-intercept b.

Step 1: Find the Slope (m)

To find the slope, we need to use the formula:

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

where (x1, y1) and (x2, y2) are two points on the line. Since we only have one point, (4, 5), we can use any other point on the line to find the slope. Let's assume the other point is (0, 0), which is the origin.

m = (5 - 0) / (4 - 0) m = 5/4

Step 2: Find the Y-Intercept (b)

To find the y-intercept, we can use the point (4, 5) and the slope m we found in Step 1. We can plug these values into the slope-intercept form equation:

5 = (5/4)(4) + b

Simplifying the equation, we get:

5 = 5 + b b = 0

The Slope-Intercept Form of the Line

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

y = (5/4)x + 0

Simplifying the equation, we get:

y = (5/4)x

And that's it! We have successfully represented the line that passes through the point (4, 5) in slope-intercept form.

Conclusion

In this article, we have shown how to represent a line that passes through the point (4, 5) in slope-intercept form. By following the steps outlined above, you can find the slope-intercept form of any line given a point on the line. Remember to always simplify your equations and double-check your work to ensure accuracy.