(-3 1) In Slope Intercept Form

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Jul 03, 2024

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Slope-Intercept Form: Understanding (-3, 1)

In algebra, the slope-intercept form is a way to express 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 point (-3, 1) in slope-intercept form.

What is the Slope-Intercept Form?

The slope-intercept form is a linear equation that can be written in the form of:

y = mx + b

Where:

• m is the slope, which represents the ratio of the vertical change to the horizontal change (rise over run).
• b is the y-intercept, which is the point at which the line crosses the y-axis.

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) of the line that passes through this point.

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

y - y1 = m(x - x1)

Where (x1, y1) is the point (-3, 1).

Rearranging the equation to solve for m, we get:

m = (y - y1) / (x - x1)

Substituting the values, we get:

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

So, the slope of the line is 0.

Now that we have the slope, we can use the slope-intercept form to write the equation of the line:

y = mx + b

Substituting m = 0, we get:

y = 0x + b

Since the point (-3, 1) lies on the line, we can substitute x = -3 and y = 1 to find the value of b:

1 = 0(-3) + b 1 = b

So, the value of b is 1.

The Final Answer

The point (-3, 1) in slope-intercept form is:

y = 0x + 1

or simply:

y = 1

This means that the line is horizontal and passes through the point (-3, 1) on the coordinate plane.