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Find the equation of a line that passes through the point (2, -1) and parallel to the line 2x - 3y + 4 = 0.
Solution:
Consider the given line
Rewrite the equation of a line in slope-intercept form as follows
The slope of a line is m1 = 2/3 and the y-intercept is b = 4/3. To draw or sketch a line, plot 4/3 at the y-axis. This is your first point of the line at (0, 4/3). Next, use the slope to get the second point. From the first point, count 3 units to the right and then 2 units upward. Connect the two points and you have now a line as follows
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| Photo by Math Principles in Everyday Life |
Finally, plot (2, -1) and draw a line parallel to the given line that contains a given point as follows
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| Photo by Math Principles in Everyday Life |
If two lines are parallel, then their slopes are equal, which is m1 = m2 = 2/3. Therefore, using the point-slope form, the equation of another line that passes through the point (2, -1) is
