Posted by Melanie on Wednesday, February 16, 2011 at 5:26pm.
A line that is parallel to y = 2 has a slope of 0.
A line perpendicular to y = 2 has a slope of infinity (or undefined).
A line parallel to x = -4 has a slope of infinity (or undefined).
A line perpendicular to x = -4 has a slope of 0.
By slope intercept form I assume you mean y = mx + c.
The first equation is y = 2. It's already in slope intercept form, just simplified.
Think of it as y = 0x + 2. Now it's easier to see that the slope of such a line is 0 and the intercept is +2. This line is a horizontal line that intercepts at (0,2).
A line perpendicular to that would therefore have a slope of infinity, or an undefined slope since it's a vertical line.
The second equation is x = -4. That means that there can be no other x value anywhere on this line than -4. It's a vertical line that only crosses the x axis. Vertical = undefined slope.
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