Find the coefficients of the equation ? 𝑥+? 𝑦 − 12 = 0 when the y-intercept = 4 and an x-intercept = −2

Question

Can I please get a step by step on how to find the answer, i would appreciate it.

Answer 1

The intercepts indicate two solutions, (0, 4) and (-2, 0)

Ax + By = 12

If x = 0, then y = 4 and B = 3

If y = 0, then x = -2 and A = -6

Answer 2

We need to find the coefficients Ax+By=12 such that the y intercept is at 4 and the x intercept is at -2. Rewriting we obtain that y=-(A/B)x+12/B. Putting x=0 we get that 4=12/B so that B=3. Putting y=0 we get 0=-(A/3)(-2)+4 so that 2A/3=-4 or A=-6. Hence, the equation of the line is -6x+3y-12=0.