Question

A line can be defined in general form by the equation Ax+By = C where A, B and C are constants. You may assume that both A and B are non-zero. Then the slope of the line is , its x intercept is , and its y intercept is . Of course your answers will depend on A, B, and C. Remember that mathematics, and WeBWorK, are case sensitive, so make sure to use upper case letters A, B and C.

Answer 1

note: I'm not going to type in case sensitive or correct grammer so it's not my fault if you paste my answer and the program says it's wrong


y=mx+b
m=slope
b=y intercept

the x intercept is where the line crosses the x axis or where y=0
the y intercept is where the line crosses the y axis or where x=0


so

for the slope, solve for y
Ax+By=C
minus Ax both sides
By=-Ax+c
divide both sides by B

`y=(-A)/(B)x+(C)/(B)`

the slope is
`(-A)/(B)` and the y intercept is at
`y=(C)/(B)`

find x intercept
set y=0

Ax+By=C
Ax+B(0)=C
Ax=C
divide both sides by A

`x=(C)/(A)`
the x intercept is at
`x=(C)/(A)` or the point
`((C)/(A),0)`


slope is
`(-A)/(B)`
the x intercept is at
`x=(C)/(A)` or the point
`((C)/(A),0)`
the y intercept is at
`y=(C)/(B)` or the point
`(0,(C)/(B))`