Write an equation of a line with x intercept 6 and y intercept 4. Final Answer in standard form.?

Write an equation of a line with x intercept 6 and y intercept 4. Write the final answer in standard form. (Ax + By = C)


I already know the answer is 2x+3y = 12, I'm just clueless as to how they got that answer (review book)

Write an equation of a line with x intercept 6 and y intercept 4. Final Answer in standard form.?
The line passes through (6, 0) and (0, 4),





m(slope) = (4 - 0)/(0 - 6) = -2/3





y = mx + c


y = (-2/3)x + 4


3y = -2x + 12


2x + 3y = 12
Reply:at the x intercept y = 0 and at the y intercept x = 0





therefore we have the points (6,0) and (0,4)





find the gradient between these two points..





rise/run = (0-4)/(6-0) = -2/3





therefore using for now the equation y = mx + c we have m = -2/3. substituting x = 0 gives y = c = 4.





we now have y = -2/3*x + 4





rearranging this becomes y + 2/3*x = 4





now mulitply through by 3 to get...





2x + 3y = 12 !!