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.

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