Let's first identify at least two points that pass through the line and generate an equation. We've identified two points at A(x1,y1) = (0,3) and B(x2,y2) = (1,1).
Let's generate the equation by getting the value of the slope (m) and y-intercept (b) then substitute it to the Slope-Intercept Formula.
[tex]\text{ m = }\frac{y_2-y_1}{x_2-x_1_{}}\text{ = }\frac{1\text{ -3}}{1\text{ -0}}\text{ = }\frac{-2}{1}=-2\text{ }[/tex]
Let's determine the value of the y-intercept (b) at m = -2 and (x,y) = (0,3).
[tex]\text{ y = mx + b }\rightarrow\text{ 3 = (-2)(0) + b }\rightarrow\text{ b = 3}[/tex]
Therefore, the formula of the line is:
[tex]\text{ y = mx + b }\rightarrow\text{ y = (-2)x + 3}[/tex][tex]\text{ y = -2x + 3 }\rightarrow\text{ 2x + y = 3}[/tex]
The shaded area is at the left side of the graph and the boundary is solid. Therefore, the inequality represented by the graph must be:
[tex]\text{ 2x + y = 3 }\rightarrow\text{ 2x + y }\leq\text{ 3}[/tex]
The given choices arent's their simplest form, it has an LCM of 7. Let's use this LCM to transform the inequality the same as the choices given. We get,
[tex]\text{2x + y }\leq\text{ 3 }\rightarrow\text{ 7(2x + y }\leq\text{ 3)}[/tex][tex]\text{ 14x + 7y }\leq21[/tex]
The answer is letter C.
