How do you know when a parabola is a "smiley face" or "frown face"?
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Answer:
1. Not possible. The slope of such a line is undefined. Its equation is x=7.
2. y = 3x -2
3. The slope is undefined. (The line is a vertical line.)
Step-by-step explanation:
1. The y-axis is a vertical line. Computing the slope of such a line involves division by zero, an operation that is undefined. Since the line is parallel to the y-axis, there is no y-intercept.
In slope-intercept form, the equation would be useless:
... y = (undefined)x + (no such value)
If your point is supposed to be (7, 8)*, the more useful equation is the "standard form" equation:
... x = 7
2. The slope of the perpendicular line is the negative reciprocal of this:
... m = -1/(-1/3) = 3
In point-slope form, the equation of the perpendicular line through the given point is ...
... y = 3(x -2) +4
... y = 3x -2 . . . . . . . . simplified to slope-intercept form
3. The slope is computed from ...
... m = (change in y)/(change in x) = (-3 -4)/(-1 -(-1)) = -7/0 = undefined
The slope is undefined. This tells you the line is a vertical line. Its location is the x-value of the points, ...
... x = -1
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* If your point is really (77, 88), then the line has equation x = 77.
