Answers:
- a) x = -5
- b) x = 1
- c) y = 3
- d) y = -2
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Explanation:
Line A is vertical and it goes through -5 on the x axis. Every point on this vertical line has the same x coordinate. Since all x coordinates are -5, but y can vary, this means the equation of this vertical line is x = -5.
Line B is a similar story, but now x = 1 is the equation for line B. Two points on line B are (1,2) and (1,5); both of which have x coordinate of 1.
In general, the equation of any vertical line is always of the form x = k, where k is some real number.
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For horizontal lines, the general form is y = k, for some real number k.
Line C has the equation y = 3 because two points like (0,3) and (1,3) are on this horizontal line. We can think of y = 3 as y = 0x+3, showing this horizontal line (and any horizontal line) has the slope 0. The slope of any vertical line is undefined.
The equation for line D is y = -2. We can write that as y = 0x-2, but it's easier to stick with y = -2. All points on line D have the same y coordinate -2.
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To summarize:
- The equation for line A is x = -5
- The equation for line B is x = 1
- The equation for line C is y = 3
- The equation for line D is y = -2
- Vertical lines are of the form x = k. The slope is undefined.
- Horizontal lines are of the form y = k. The slope is 0.
