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Question 504370: How do you draw a line that passes through the origin and has slope 5/3
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Slope is defined as the rise (or the vertical change) divided by the run (change in the horizontal direction moving to the right).
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The problem tells you that one point on the graph is the origin. It also tells you that the slope is 5/3. The divisor is the run or denominator. The rise is the numerator. Therefore, beginning at the origin, move horizontally (along the x-axis) 3 units. Stop there. (You are at the point +3 on the x-axis). From that point move up vertically +5 units in the y direction. That puts you at the (x,y) point (3,5). Stop there and mark this point. Now draw a line that connects the origin to the point (3,5) and continue this line in both directions ... that is you graph a line that extends through the points (0,0) and (3,5).
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That's it. Just remember what slope means ... rise/run ... Then all you need is one point on the graph and from that point you can move horizontally the amount of the run (denominator), stop there and then go vertically the amount of the rise.
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A point to know. If the slope is a whole number, you can set it up as a rise over run ratio by using 1 as the denominator. For example, if you are given a slope of 10 you can write it as 10/1 so that for every 1 unit you move horizontally to the right (per the denominator or run) from a point on the line, you stop and then move up 10 units (per the numerator).
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Also, if you have a negative slope, that means the numerator (rise) actually is negative or moves down. For example. given a slope of -2/3, start at a known point on the graph and move 3 units horizontally to the right, then stop and go DOWN 2 units vertically. Mark that end point and draw a line that extends from the starting point and goes through the end point you found.
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In general you can say that a graph that has a positive slope will slant up as you move to the right. And a graph that has a negative slope will slant down as you move to the right.
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Hope this helps you to understand the problem. A little practice and it will become second nature to you.
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