(-4 5) And (0 3) In Slope Intercept Form

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Jul 03, 2024

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Graphing Linear Equations: Writing (-4, 5) and (0, 3) in Slope-Intercept Form

In graphing linear equations, it's essential to understand how to write points in slope-intercept form. 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'll explore how to write the points (-4, 5) and (0, 3) in slope-intercept form.

Point (-4, 5) in Slope-Intercept Form

To write the point (-4, 5) 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.

Given the point (-4, 5), we can set x1 = -4 and y1 = 5. Now, we need to find the slope (m). Let's use another point on the line, say (0, 3). Using the slope formula, m = (y2 - y1) / (x2 - x1), we get:

m = (3 - 5) / (0 - (-4)) m = (-2) / 4 m = -1/2

Now that we have the slope, we can write the point-slope form:

y - 5 = (-1/2)(x + 4)

To convert this to slope-intercept form, we can simplify the equation:

y = (-1/2)x + 2

So, the point (-4, 5) in slope-intercept form is y = (-1/2)x + 2.

Point (0, 3) in Slope-Intercept Form

Using the same process, let's find the slope-intercept form for the point (0, 3). We can use the point (-4, 5) to find the slope (m). Again, using the slope formula:

m = (5 - 3) / (-4 - 0) m = 2 / -4 m = -1/2

Now, we can write the point-slope form:

y - 3 = (-1/2)(x - 0)

Simplifying the equation, we get:

y = (-1/2)x + 3

So, the point (0, 3) in slope-intercept form is y = (-1/2)x + 3.

Conclusion

In this article, we've seen how to write the points (-4, 5) and (0, 3) in slope-intercept form. By finding the slope and y-intercept, we can express these points in the form of y = mx + b. Understanding slope-intercept form is essential in graphing linear equations and solving various problems in mathematics.