Question

Find the x-intercepts and y-intercepts of a line passing through point (2,a) and (6,12)

Answer 1

Answer:

X INTERCEPT IS (a-36)/(a-12).

Y INTERCEPT IS (a-36)/3.

Step-by-step explanation:

$(2 \: \: \: a) \: \: \: \: \: (6 \: \: \: \: \: 12) \\ \\ equation \: of \:l ine \: is \: \: \: (y - 12) = (\frac{a - 12}{2 - 6} )(x - 6) \\ \\ - 3(y - 12) = (a - 12)(x - 6) \\ \\ (a - 12)(x - 6) + 3(y - 12) = 0 \\ \\ (a - 12)x + 3y - 6(a - 12) - 36 = 0 \\ \\ (a - 12)x + 3y = a - 72 + 36 = 0 \\ \\ (a - 12)x + 3y = (a - 36) \\ \\ put \: \: x = 0 \: \: \: \: \: \: \: \: \: \: 3y = (a - 36) \\ \\ y = \frac{(a - 36)}{3} . \\ \\ therefore \: \: \: y \: intercept \: is \: \: \: \frac{(a - 36)}{3}. \\ \\ \\ \\ put \: \: \: y = 0 \\ \\ \\ \: \: (a - 12)x = (a - 36) \\ \\ x = \frac{ (a - 36)}{(a - 12)} . \\ \\ x \: intercept \: is \: \frac{ (a - 36)}{(a - 12)}.$