The general equation of a line id expressed as
[tex]\begin{gathered} y\text{ = mx + c ---- equation 1} \\ where \\ m\Rightarrow slope\text{ of the line} \\ c\Rightarrow y-intercept\text{ of the line} \end{gathered}[/tex]
Given that a line equation to be
[tex]2x\text{ + 5y = 10 ---- equation 2}[/tex]
Step 1:
From equation 2, make y the subject of the formula.
[tex]\begin{gathered} 2x+5y\text{ = 10} \\ subtract\text{ }2x\text{ from both sides of the equation} \\ 2x-2x+5y\text{ = 10-2x} \\ 5y\text{ = 10 - 2x} \\ divide\text{ both sides of the equation by the coefficient of y, which is 5.} \\ \text{thus,} \\ \frac{5y}{5}\text{ = }\frac{\text{10-2x}}{5} \\ \Rightarrow y\text{ = 2-}\frac{2}{5}x\text{ ---- equation 3} \\ \end{gathered}[/tex]
Step 2:
Compare equations 1 and 3.
[tex]\begin{gathered} \text{Equation 1: y = mx + c} \\ \text{Equation 3: y = -}\frac{2}{5}x+2 \end{gathered}[/tex]
comparing both equations,
[tex]m\text{ = -}\frac{2}{5}\text{ = -0.40, c=2}[/tex]
Hence, the slope of the line is -0.40 (2 decimal places).
