(-3 6) (0 0) In Slope Intercept Form

Suzhoumeite

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Jul 03, 2024

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Converting a Point-Slope to Slope-Intercept Form: (-3, 6) and (0, 0)

In algebra, we learn about different forms of linear equations, including point-slope form and slope-intercept form. In this article, we will explore how to convert a point-slope form to slope-intercept form using the points (-3, 6) and (0, 0).

Point-Slope Form

The point-slope form of a linear equation is given by:

$y - y_1 = m(x - x_1)$

where $(x_1, y_1)$ is a point on the line, and $m$ is the slope of the line.

Slope-Intercept Form

The slope-intercept form of a linear equation is given by:

$y = mx + b$

where $m$ is the slope of the line, and $b$ is the y-intercept.

Converting Point-Slope to Slope-Intercept Form

To convert a point-slope form to slope-intercept form, we need to use the point-slope form equation and manipulate it to get the slope-intercept form equation.

Let's use the point (-3, 6) to convert the point-slope form to slope-intercept form.

Using the Point (-3, 6)

Given the point (-3, 6), we can write the point-slope form equation as:

$y - 6 = m(x + 3)$

To convert this to slope-intercept form, we can start by distributing the $m$ to the terms inside the parentheses:

$y - 6 = mx + 3m$

Now, we can add 6 to both sides of the equation to get:

$y = mx + 3m + 6$

This is the slope-intercept form of the equation, where $m$ is the slope, and $3m + 6$ is the y-intercept.

Using the Point (0, 0)

Given the point (0, 0), we can write the point-slope form equation as:

$y - 0 = m(x - 0)$

Simplifying the equation, we get:

$y = mx$

This is the slope-intercept form of the equation, where $m$ is the slope, and the y-intercept is 0.

Conclusion

In this article, we have seen how to convert a point-slope form to slope-intercept form using the points (-3, 6) and (0, 0). By manipulating the point-slope form equation, we can get the slope-intercept form equation, which is a more useful form for graphing and analyzing linear equations.