How is $-4/7$ the slope of $4x+7y=1$?

Question

How is $-4/7$ the slope of $4x+7y=1$?

Can someone explain? I think they have divided the coefficients of $x$ and $y$.

Answer 1

It is a bit of algebra, but essentially you have:

$4x+7y=1,$

$7y=-4x+1,$

$y=-4/7x+1/7$

the slope is always a coefficient of the term containing $x$.

Answer 2

Hints:- For a linear equation $ax+by=c$, slop is always $-\dfrac{a}{b}$.

Answer 3

There’s another neat way to think about slopes. Suppose $x$ is increased by $1$ unit. How should $y$ change so that that the resulting point is still on the line, i.e. the equation remains unchanged? The new LHS is $$4(x+1) +7y = 4x+7y +4 $$ If $y$ is decreased by $\frac 47$, the change in $x$ cancels out: $$4x+7(y-\frac 47) +4 = 4x +7y -4+4 =4x+7y $$

The slope is therefore $-\frac 47$.