Math: Linear Equations

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What is "3x=9" in y=mx+b form, and what is its slope, y-intercept, and x-intercept? [i think that its x-intercept is (3,0), but i'm not sure about any of the others]

Also, what is the x-intercept of "2y+16=0"? [is it "none"?]

  • Math: Linear Equations -

    I think these are trick questions and you have the right idea.

    3x = 9 is the equation of a vertical line. There is no y in the equation, so there is no "y = mx + b" form for a vertical line. The simplest way to express this line is x = 3.

    Its x-intercept is 3 (because (3, 0) is where the line crosses the x-axis).

    It does not have a y-intercept, because the line never crosses the y-axis.

    Technically, it has an undefined slope.

    Similarly, the other equation is a horizontal line. 2y + 16 = 0 is the same as 2y = -16, or y = -8. This is a horizontal line through (0, -8). It has no x-intercept. The y-intercept is -8. The slope is zero. I think you are right to say that the x-intercept is "none."

  • Math: Linear Equations -

    Thanks!!! No wonder why these questions didn't make much sense and didn't seem quite possible to solve...

  • Math: Linear Equations -

    However, if the equation was this instead ...

    2y + 16x = 0

    ... then you do have a diagonal line that has both an x-intercept and a y-intercept and a slope that is not zero but not undefined. I think it is a negative slope.

    Can you figure out the x-intercept of the line? the y-intercept of the line? and the slope of the line? Hint: When y = 0, what is x? That gives you one intercept. When x = 0, what is y? That gives you another intercept. Draw the line and see if you can find the slope.

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