Question

Find the slope of the line given by the equation $2x+4y=10$.

Answer 1

Step 1: Convert the given equation into its standard form.

The standard form of linear equation is $y=mx+c$.

$$\begin{gathered} \Rightarrow 2x+4y=10 \\ \Rightarrow 4y=10-2x \\ \Rightarrow y=\frac{10-2x}{4} \\ \Rightarrow y=\frac{10}{4}-\frac{x}{2} \\ \Rightarrow y=-\frac{x}{2}+\frac{10}{4} \end{gathered}$$

Step 2: Comparing the above equation with standard form.

The coefficient of $x$, i.e., $m$, is the slope of the line. Comparing with standard equation,

$\therefore m=-\frac{1}{2}$.

Hence, slope of the line is $-\frac{1}{2}$.