(-1 2) And (6 3) In Slope Intercept Form

Suzhoumeite

4 min read Jul 03, 2024

Representing (-1, 2) and (6, 3) in Slope-Intercept Form

In this article, we will explore how to represent the points (-1, 2) and (6, 3) in slope-intercept form.

What is Slope-Intercept Form?

The 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 (how steep it is)
b represents the y-intercept (the point where the line crosses the y-axis)

Representing (-1, 2) in Slope-Intercept Form

To represent the point (-1, 2) in slope-intercept form, we need to find the slope (m) and the y-intercept (b) of the line that passes through this point.

Let's assume that the equation of the line is in the form of y = mx + b. We can plug in the point (-1, 2) into the equation to get:

2 = m(-1) + b

Simplifying the equation, we get:

2 = -m + b

Now, we need to find the value of m and b. Since we only have one point, we cannot find a unique solution. However, we can express the equation in terms of m and b.

For example, if we let m = 1, then we can find the value of b:

2 = -1 + b b = 3

So, one possible equation that passes through the point (-1, 2) is y = x + 3.

Representing (6, 3) in Slope-Intercept Form

To represent the point (6, 3) in slope-intercept form, we can follow the same steps as before.

Let's assume that the equation of the line is in the form of y = mx + b. We can plug in the point (6, 3) into the equation to get:

3 = m(6) + b

Simplifying the equation, we get:

3 = 6m + b

Again, we need to find the value of m and b. Since we only have one point, we cannot find a unique solution. However, we can express the equation in terms of m and b.

For example, if we let m = 0, then we can find the value of b:

3 = 0 + b b = 3

So, one possible equation that passes through the point (6, 3) is y = 3.

Conclusion

In this article, we have seen how to represent the points (-1, 2) and (6, 3) in slope-intercept form. We found that one possible equation that passes through the point (-1, 2) is y = x + 3, and one possible equation that passes through the point (6, 3) is y = 3. Note that these are not unique solutions, and there may be other equations that pass through these points as well.