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Chapter 0: Problem 41

Write the equation in the slope-intercept form, and then find the slope and \(y\) -intercept of the corresponding lines. $$ \sqrt{2} x-\sqrt{3} y=4 $$

Short Answer

Expert verified
The equation in slope-intercept form is \(y = \frac{\sqrt{2}}{\sqrt{3}}x - \frac{4}{\sqrt{3}}\). The slope (m) is \(\frac{\sqrt{2}}{\sqrt{3}}\) and the y-intercept (b) is \(-\frac{4}{\sqrt{3}}\).

Step by step solution

01

Rewrite the equation in the slope-intercept form

To write the given equation, \(\sqrt{2} x-\sqrt{3} y = 4\), in the slope-intercept form, we need to isolate y: \(-\sqrt{3}y = -\sqrt{2}x + 4\) Divide both sides of the equation by \(-\sqrt{3}\): \(y = \frac{\sqrt{2}}{\sqrt{3}}x - \frac{4}{\sqrt{3}}\)
02

Identify the slope(m) and y-intercept (b)

Now that the equation is in the slope-intercept form, we can easily identify the slope and y-intercept: \(y = \frac{\sqrt{2}}{\sqrt{3}}x - \frac{4}{\sqrt{3}}\) Comparing the equation with \(y = mx + b\), we can determine the values of m and b: Slope (m): \(\frac{\sqrt{2}}{\sqrt{3}}\) Y-intercept (b): \(-\frac{4}{\sqrt{3}}\) Thus, the slope of the line represented by the given equation is \(\frac{\sqrt{2}}{\sqrt{3}}\) and the y-intercept is \(-\frac{4}{\sqrt{3}}\).

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