9514 1404 393
Answer:
see attached
Explanation:
First of all, you must be completely comfortable plotting points on a graph, and reading the coordinates of a point.
Second, you need to understand that "slope" or "rate of change" is the ratio "rise over run". In this context, "rise" is the vertical change, and "run" is the horizontal change. Typically "run" is left to right, so is in the +x direction. "Rise" is positive if the line slopes upward toward the right, and negative if the line slopes downward.
A vertical line has a "run" of zero, so you end up with rise/0, which is "undefined." Whenever you see "undefined" as the slope, it means the line is vertical. (Its equation is x=constant.)
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With these things in mind, you work this problem by first plotting the point (4, 3). Then for each of the given slopes, you identify a suitable "rise" and "run" that will get you to another point on the line. Draw the line through the original point and the point you found.
(a) rise/run = 1, so you go the same number of grid squares up as you do to the right.
(b) rise/run = -2, so you go down 2 grid squares for each 1 to the right.
(c) rise/run = -3/2, so you go down 3 grid squares for each 2 to the right.
(d) "undefined" means the line is vertical. The x-value of the given point is 4, so the vertical line has equation x=4. You draw it through the given point.
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Additional comment
Here, we use our understanding of slope to draw the line on the graph. Other times, you will need to use your understanding of slope to figure out what the slope is of a line plotted on a graph. It is usually useful to identify points on the line where it crosses grid intersections. That way, computation of rise and run do not involve any guessing as to what the coordinates are.
