[tex]\begin{gathered} \text{The equation of the line is ;} \\ y\text{ =}-2x\text{ + 4} \end{gathered}[/tex]
Here, we want to get the equation that best represents the line on the graph
Generally, the equation of a straight line can be represented as;
[tex]y\text{ = mx + b}[/tex]
where m is the slope and b is the y-intercept
The y-intercept is the point at which the line touches the y-axis
From the graph, the point is at y = 4
So the partial equation is;
[tex]y\text{ = mx + 4}[/tex]
To write the full equation, we need the value of m which is the slope
To get this, we need a point on the graph
We can identify the point (2,0)
So in this case, we substitute 2 for x and 0 for y
Doing this, we have;
[tex]\begin{gathered} 0\text{ = 2(m) + 4} \\ \\ 2m\text{ = -4} \\ \\ m\text{ = }\frac{-4}{2} \\ m\text{ = -2} \end{gathered}[/tex]
So the equation of the line is;
[tex]y\text{ = -2x + 4}[/tex]
