Graph of lines going through the origin

[mech-eng]

Here is an explanation about drawing the graphs of linear lines which, I think, incorrect. So would you check it?

"If graph, such as y=7x, goes through the origin, it has only one intercept, and other points will be needed for graphing." I think other points will not be needed because lines such as y=7x can easily be plotted.

Source: Algebra and Trigonometry by Keedy/Bittinger 4th edition.

Thank you.

 

[scottdave]

I think what they are trying to say is if you get two points, then you can just connect the dots. For example this line: y = 7x + 14. Set y equal zero to get the x intercept at (-2,0) then set x equal to zero to get the y intercept at (0,14). Then just get a straight edge and connect the two points.

With something like y = 7x, you will have to plug in another value for x or y and calculate an extra point {the origin is one of the points on the line}. I think that is what they mean by "other points will be needed".

 

[mech-eng]

You are right but I thought it could be drawn if we caught the right direction or angle.

Thank you.

 

[scottdave]

Still, if you say that you are going to move in the direction of slope 7, you would move to the right 1 unit and up 7 units. This in effect creates another point on the line. It's not that the book is absolutely wrong. What the book described is one way to plot the line.

 

[fresh_42]

You are right but I thought it could be drawn if we caught the right direction or angle.

Thank you.

Yes. And how do you use direction or angle? You use them to find a way to place your ruler, that gives you a second point somehow.

 

[mech-eng]

Still, if you say that you are going to move in the direction of slope 7, you would move to the right 1 unit and up 7 units. This in effect creates another point on the line. It's not that the book is absolutely wrong. What the book described is one way to plot the line.

But if you somebody do it by pencil, I think they would not create a once more point, they draw a part of the line and they would have created infinitely many points.

Thank you.

 

[Nidum]

To place a straight line on a graph you just need the coordinates of any two well separated points on that line .

 

[Mark44]

"If graph, such as y=7x, goes through the origin, it has only one intercept, and other points will be needed for graphing." I think other points will not be needed because lines such as y=7x can easily be plotted.

What they're saying here is that lines of the form y = mx, with m ≠ 0, have the x-intercept and the y-intercept at the same point -- the origin. In contrast, the line y = 2x + 4 has intercepts at different places, making it easier to graph the line.

For the equation y = 7x, one point is at (0, 0), and it's easy to get another point by substituting a value for x, and calculating the y value. Doing this, we can see that the graph goes through (1, 7) and (2, 14). Any value you put in for x gives a corresponding y-value.