Question 181846
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Your first equation is in slope-intercept form:


*[tex \LARGE \text{          }\math y = mx + b]


where <i>m</i> is the slope and <i>b</i> is the <i>y</i>-intercept meaning the point (0,b) where the line intersects the <i>y</i>-axis.


You need to arrange your second equation into the same form, so that you can see the slope and <i>y</i>-intercept of the second equation.



Use the following rules:


*[tex \LARGE \text{          }\math L_1 \parallel L_2 \ \ \Leftrightarrow\ \ m_1 = m_2]


*[tex \LARGE \text{          }\math L_1 \perp L_2 \ \ \Leftrightarrow\ \ m_1 = -\frac{1}{m_2}]


If the slopes AND <i>y</i>-intercepts of the two equations are the same, they are equations of the same line.


If the slopes are equal but the <i>y</i>-intercepts are different, they are equations of two different parallel lines.


If the slopes are negative reciprocals of one another, then the lines are perpendicular.


If none of the above relationships hold, then they are not the same, not parallel, and not perpendicular.






John
*[tex \LARGE e^{i\pi} + 1 = 0]
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