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.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

Given the first line has a slope of 10 and an x-intercept of (s, 0). Therefore, if the coordinate of the x-intercept and slope is substituted in the equation of line. Then, the equation can be written as,

y = mx + c

0 = 10s + c

c = -10s

Also, given the second line has a slope of 6 and an x-intercept of (t, 0). Therefore, if the coordinate of the x-intercept and slope is substituted in the equation of line. Then, the equation can be written as,

y = mx + c

0 = 6t + c

c = -6t

Further, since the y-intercept of the line is equal for both the line, therefore, we can write,

c = c

-10s = -6t

s/t = -6/-10

s/t = 3/5

Hence, the ratio of s to t is 3/5.

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