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23 May, 23:13

Two lines have the same non-zero $y$-intercept. The first line has a slope of 10 and an $x$-intercept of $ (s, 0) $. The second line has a slope of 6 and an $x$-intercept of $ (t, 0) $. What is the ratio of $s $ to $t$? Express your answer as a common fraction.

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  1. 23 May, 23:14
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    t / s = 5 / 4

    Explanation:

    The intercept form of st line is

    x / a + y/b = 1 where a and b are intercept on x and y axis respectively

    Let common y intercept be b.

    For first line

    a = s,

    x / s + y / b = 1

    y / b = - x / s + 1

    y = - b / s x + b

    Slope of the line given is 10 so

    - b / s = 10

    Similarly we can write, for second line

    - b / t = 8

    Dividing them

    t / s = 10 / 8

    t / s = 5 / 4
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