Answer:
5x+4y=24
Explanation:
So Ax+By=C is the standard form equation of a line.
y=mx+b (in which m is the slope and b is the y-intercept) is the equation that most people start off with.
Since the line intersects the y-axis at (0,6), the y-intercept is 6.
So, we can substitute 6 with b, which is y=mx+6.
Now, we can find the slope (m) by either inserting a known point (x,y) or using rise/run. Either way, you get the slope as -5/4 because we go five units DOWN and four units RIGHT from (0,6), one known point, to (4,1), another known point.
The y=mx+b equation becomes: y=(-5/4)x+6.
Now, we subtract (-5/4)x on both sides to get (5/4)x+y=6
Multiply 4 on both sides because standard form requires no fractions or decimals.
The final answer is 5x+4y=24.
That's your answer, fully simplified!