Ax+by=c is a straight line. When b=0 then it is // to y-axis

[CynicusRex]

Am I forgetting some critical basic knowledge?
It says: In the plane (identified by R^2) a linear equation ax+by=c is a straight line. If b=0 then this straight line is parallel with the y-axis; in the other case it is a straight line with slope -a/b. A (2 by 2)-system linear equation.

Why is it parallel? If you make b=0 in ax+by=c you still get a straight line. Or should I see it as: b y = -ax + c

 

[SteamKing]

Is this a mistake in the textbook or am I forgetting some critical basic knowledge?
It says: In the plane (identified by R^2) a linear equation ax+by=c is a straight line. If b=0 then this straight line is parallel with the y-axis; in the other case it is a straight line with slope -a/b.

Take the equation for the line and set b = 0. Solve for x. What do you get?

Since there are three constants here, namely a, b, and c, the 'other case' is not clear, since we have discussed what happens when b = 0. In any event, take the original equation for the line and set a = 0 or c = 0 and see what remains.

 

[ehild]

Is this a mistake in the textbook or am I forgetting some critical basic knowledge?
In the plane (identified by R^2) a linear equation ax+by=c is a straight line. If b=0 then this straight line is parallel with the y-axis;
Why is it parallel? If you make b=0 in ax+by=c you still get a straight line.

If a line is parallel with a straight line, is not it a straight line?
If b=0 ax=-c, this is a straight line, but where? Does it intercept the y axis? So is this line parallel with the y-axis (or coincide with it) ?

 

[CynicusRex]

I'm literally speechless on how I missed that. I'm incredibly rusty in the basics of math. I thought ax = c was the same as ax + 0 = y.
I didn't figure c as a constant.

 

[ehild]

a, b, c are all constants.

 

[CynicusRex]

I'm used to seeing y on the other side of the equation symbol (as slope intercept form). That's why I thought on c being just another solution variable.
Anyway, thank you. Can't wait for feeling bad on the next blunder.

 

[SammyS]

I'm used to seeing y on the other side of the equation symbol (as slope intercept form). That's why I thought on c being just another solution variable.
Anyway, thank you. Can't wait for feeling bad on the next blunder.

By the way:

Welcome to PF !