We have seen that the gradient intercept form of a line looks like this:
From this form we can:
Another useful form for the equation of a straight line is the general form. It looks like this:
In this form:
Notice that in this form, the $y$y-intercept cannot be seen in the equation. We would have to substitute $x=0$x=0 to find it.
The advantages of writing an equation in this form can be seen when:
We can convert from one form to another by rearranging the equation. Rearranging the equation is just like solving an equation: we carry out inverse operations to move terms from one side to another, or to change the sign from positive to negative. Let me show you what I mean.
Rearrange $y=4x-8$y=4x−8 into general form.
Move all the terms to the same side, remembering to keep the coefficient of $x$x positive.
Rearrange $3x-6y+12=0$3x−6y+12=0 into gradient-intercept form.
To make $y$y the subject, we need to move the $x$x term and the constant to the other side. It would be preferable to keep the coefficient of $y$y positive.
We can now divide through by $6$6 to make $y$y the subject.
Which line is steeper, $2x+3y-2=0$2x+3y−2=0 or $2x+5y+3=0$2x+5y+3=0?