Given:
Given that the graph of the linear equation.
We need to determine the equation of the graph.
Slope:
The slope of the equation can be determined using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let us substitute the coordinates (2,0) and (0,-4) in the above formula, we get;
[tex]m=\frac{-4-0}{0-2}[/tex]
[tex]m=\frac{-4}{-2}[/tex]
[tex]m=2[/tex]
Thus, the slope of the equation is 2.
y - intercept:
The y - intercept of the equation is the value of y when x = 0.
Hence, from the graph, it is obvious that when x = 0, the value of y is -4.
Therefore, the value of the y - intercept is b = -4.
Equation of the line:
The equation of the line can be determined using the formula,
[tex]y=mx+b[/tex]
Substituting the values, we have;
[tex]y=2x-4[/tex]
Subtracting both sides by 2x, we have;
[tex]-2x+y=-4[/tex]
Dividing both sides by -1, we get;
[tex]2x-y=4[/tex]
Thus, the equation of the line is [tex]2x-y=4[/tex]
Hence, Option B is the correct answer.
