(3 1) And (0 10) In Slope Intercept Form

5 min read Jul 03, 2024

Understanding (3, 1) and (0, 10) in Slope-Intercept Form

In algebra, the slope-intercept form is a way of expressing a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept. In this article, we will explore how to write the points (3, 1) and (0, 10) in slope-intercept form.

What is the 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 (a measure of how steep the line is)
b is the y-intercept (the point at which the line crosses the y-axis)
x is the independent variable
y is the dependent variable

Writing (3, 1) in Slope-Intercept Form

To write the point (3, 1) in slope-intercept form, we need to find the slope (m) and the y-intercept (b).

Let's use the point-slope form, which is:

y - y1 = m(x - x1)

where (x1, y1) is the point, and m is the slope.

Using the point (3, 1), we can rewrite the equation as:

y - 1 = m(x - 3)

To find the slope (m), we need another point. Let's say we have another point, (0, 4). We can use these two points to find the slope:

m = (y2 - y1) / (x2 - x1) = (4 - 1) / (0 - 3) = 3 / -3 = -1

Now that we have the slope, we can rewrite the equation in slope-intercept form:

y = -1x + b

To find the y-intercept (b), we can plug in the point (3, 1):

1 = -1(3) + b 1 = -3 + b b = 4

So, the equation in slope-intercept form is:

y = -x + 4

Writing (0, 10) in Slope-Intercept Form

Using the same approach, let's write the point (0, 10) in slope-intercept form.

The point-slope form is:

y - y1 = m(x - x1)

Using the point (0, 10), we can rewrite the equation as:

y - 10 = m(x - 0)

To find the slope (m), we need another point. Let's say we have another point, (1, 8). We can use these two points to find the slope:

m = (y2 - y1) / (x2 - x1) = (8 - 10) / (1 - 0) = -2 / 1 = -2

Now that we have the slope, we can rewrite the equation in slope-intercept form:

y = -2x + b

To find the y-intercept (b), we can plug in the point (0, 10):

10 = -2(0) + b 10 = b b = 10

So, the equation in slope-intercept form is:

y = -2x + 10

Conclusion

In this article, we learned how to write the points (3, 1) and (0, 10) in slope-intercept form. By finding the slope and the y-intercept, we can express a linear equation in the form of y = mx + b.