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Math Help - Intercepts of graphs

  1. #1
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    Intercepts of graphs

    Could somebody please give me a second opinion on the correct way to write and explain intercepts.

    I have a question which asks me to find the x and y intercepts of a line which I found previously, showing each step of my method.

    My coordinates are (-4, -2) and (2, 7)

    I worked out my intercepts are (-2.7, 4), so should I say something like;

    The x and y intercepts are (-2.7) and (4), where the points corresponding to these are my coordinates as above, or

    When x = 0, then ( - 2.7, 0) and when y = 0, then (0, 4), which does not sound right to me because x = 0 then = - 2.7 seems wrong?

    Please advise
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  2. #2
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    Quote Originally Posted by David Green View Post
    Could somebody please give me a second opinion on the correct way to write and explain intercepts.

    I have a question which asks me to find the x and y intercepts of a line which I found previously, showing each step of my method.

    My coordinates are (-4, -2) and (2, 7)

    I worked out my intercepts are (-2.7, 4), so should I say something like;

    The x and y intercepts are (-2.7) and (4), where the points corresponding to these are my coordinates as above, or

    When x = 0, then ( - 2.7, 0) and when y = 0, then (0, 4), which does not sound right to me because x = 0 then = - 2.7 seems wrong?

    Please advise
    The y-intercept occurs where x = 0 and so the coordinates have the form (0, ...).
    The x-intercept occurs where y = 0 and so the coordinates have the form (...., 0).

    With the exception of your last line, you have given no answers that resemble this. And without the equation it's impossible to know whether or not the answers in your last line are correct.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    The y-intercept occurs where x = 0 and so the coordinates have the form (0, ...).
    The x-intercept occurs where y = 0 and so the coordinates have the form (...., 0).

    With the exception of your last line, you have given no answers that resemble this. And without the equation it's impossible to know whether or not the answers in your last line are correct.
    Having drawn the graph and looking on the graph where the line intercepts the x and y axis, the origin 0 has no bearing on this. The straight line graph intercepts the x axis at -2.7 and the y axis at 4. Not sure why in maths it is worded this way as you put it above;

    y-intercept occurs where x = 0 coordinates (0,...) and x-intercept occurs where y = 0 corrodinates (...,0)

    In our course book it says;

    Where the line crosses the x axis, and the y intercept is the value where the line crosses the y axis, in other words the x intercept is the value of x when y = 0, and the y-intercept is the value of y when x =0.

    This is confusing because the book does not explain the reason behind why this is a standard. Looking at the graph when x = -2.7 y= 4 these according to our book example are the intercepts.

    So based on above, y-intercept occurs where x=0 corrodinates (0, - 4)
    x-intercept occurs where y=0 corrodinates (-2.7, 0)

    Books don't seem to explain things very well to me?
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  4. #4
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    Quote Originally Posted by David Green View Post
    Having drawn the graph and looking on the graph where the line intercepts the x and y axis, the origin 0 has no bearing on this. The straight line graph intercepts the x axis at -2.7 and the y axis at 4. Not sure why in maths it is worded this way as you put it above;

    y-intercept occurs where x = 0 coordinates (0,...) and x-intercept occurs where y = 0 corrodinates (...,0)

    In our course book it says;

    Where the line crosses the x axis, and the y intercept is the value where the line crosses the y axis, in other words the x intercept is the value of x when y = 0, and the y-intercept is the value of y when x =0.

    This is confusing because the book does not explain the reason behind why this is a standard. Looking at the graph when x = -2.7 y= 4 these according to our book example are the intercepts.

    So based on above, y-intercept occurs where x=0 corrodinates (0, - 4)
    x-intercept occurs where y=0 corrodinates (-2.7, 0)

    Books don't seem to explain things very well to me?
    Mr. Fantastic is correct in his definition. Most people (and pretty much all the texts I've seen) tend to forget that, for example, a y-intercept is a point not a value. As a concrete example of this that you've seen, consider the equation y = mx + b. b is referred to as the y-intercept. The y-intercept is actually the point on the line (0, b), not b itself. It's done as a method of "shorthand" but I find it to be confusing.

    Similarly an x-intercept has the form (a, 0).

    According to this your x-intercept is (-2.7, 0) and your y-intercept is (0, -4).

    -Dan
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  5. #5
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    Quote Originally Posted by topsquark View Post
    Mr. Fantastic is correct in his definition. Most people (and pretty much all the texts I've seen) tend to forget that, for example, a y-intercept is a point not a value. As a concrete example of this that you've seen, consider the equation y = mx + b. b is referred to as the y-intercept. The y-intercept is actually the point on the line (0, b), not b itself. It's done as a method of "shorthand" but I find it to be confusing.

    Similarly an x-intercept has the form (a, 0).

    According to this your x-intercept is (-2.7, 0) and your y-intercept is (0, -4).

    -Dan
    Dan what you said above I think you made a mistake?

    Notice that an intercept is a value and not a point

    David
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  6. #6
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    Quote Originally Posted by David Green View Post
    Could somebody please give me a second opinion on the correct way to write and explain intercepts.

    I have a question which asks me to find the x and y intercepts of a line which I found previously, showing each step of my method.

    My coordinates are (-4, -2) and (2, 7)

    I worked out my intercepts are (-2.7, 4), so should I say something like;
    The difficulty is that what you have written looks like the point (x,y)= (-2.7, 4) which is, of course not near either the x or y axes.

    The x and y intercepts are (-2.7) and (4), where the points corresponding to these are my coordinates as above, or

    When x = 0, then ( - 2.7, 0) and when y = 0, then (0, 4), which does not sound right to me because x = 0 then = - 2.7 seems wrong?
    No, when x= 0, y= -2.7 (I am assuming you did the arithmetic correctly) so the point is (0, -2.7) not (-2.7, 0). Similarly, when y= 0, x= 4 so the point is (4, 0) not (0, 4).

    Please advise
    I said above, that I assumed you did the arithmetic correctly but looking back I am not so sure. You said 'My coordinates are (-4, -2) and (2, 7)". Your coordinates of what? I thought at first that those were two points of the line that you were to find the intercepts for. But if so, (-2.7, 0) and (0, 4) are NOT the intercepts.
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    Quote Originally Posted by HallsofIvy View Post
    The difficulty is that what you have written looks like the point (x,y)= (-2.7, 4) which is, of course not near either the x or y axes.


    No, when x= 0, y= -2.7 (I am assuming you did the arithmetic correctly) so the point is (0, -2.7) not (-2.7, 0). Similarly, when y= 0, x= 4 so the point is (4, 0) not (0, 4).


    I said above, that I assumed you did the arithmetic correctly but looking back I am not so sure. You said 'My coordinates are (-4, -2) and (2, 7)". Your coordinates of what? I thought at first that those were two points of the line that you were to find the intercepts for. But if so, (-2.7, 0) and (0, 4) are NOT the intercepts.
    OK more confusion added for me. The previous thread to this made a mistake between the understanding of intercepts value and a point?

    So my understanding is that an intercept is where the "I'll call it a datum line" intercepts the x axis, and the point is where the intercept is read from?

    Please advise

    David
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  8. #8
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    Quote Originally Posted by David Green View Post
    OK more confusion added for me. The previous thread to this made a mistake between the understanding of intercepts value and a point?

    So my understanding is that an intercept is where the "I'll call it a datum line" intercepts the x axis, and the point is where the intercept is read from?
    but "where" is a point, not a number! No, topsquark did not make a mistake- the "x-intercept" of a line is the point, with (x,y) coordinates, where hthe line crosses the x-axis. Of course, the y-intecept must be 0 so the point must be (x, 0) but the y-intercept is still a point, not a number. Because we know the y coordinate is 0, it is often sufficient to give just the x value but be careful about that. Certainly, doing what you did initially, writing the x intercept, x_i, and the y-intercept, y_i, together, (x_i, y_i), is wrong- that means a single point with x coordinate x_i and y coordinate _i.

    Please advise

    David
    Sometimes people will say "the x-intercept is at x= 3", say, but what they mean is the x-intercept is (3, 0).
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  9. #9
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    Quote Originally Posted by David Green View Post
    OK more confusion added for me. The previous thread to this made a mistake between the understanding of intercepts value and a point?

    So my understanding is that an intercept is where the "I'll call it a datum line" intercepts the x axis, and the point is where the intercept is read from?

    Please advise

    David
    You need to get one-on-one help from your teacher.
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