The required equation to represent the relation between the x an y is [tex]y = -\dfrac{3}{4}x - 3[/tex] . And option (A) is correct.
The given problem is based on the graphical representation of linear equation. The mathematical equation between the two variables (say x and y), where a straight line is obtained on the graph, joining the coordinates on x-axis and y-axis is known as linear equation.
In the given graph, we can see a straight line is obtain, cutting x- axis at -4 and y- axis at -3.
Now, from this data we obtain the coordinates of points at which line cuts x and y axis respectively re, (-4, 0) and (0, -3)
Use the two-point formula of line as,
[tex]y-y_{1} = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}} \times (x-x_{1})\\\\\\y-0 = \dfrac{-3-0}{0-(-4)} \times (x-(-4)})\\\\\\y = \dfrac{-3}4} \times (x+4})\\\\y = -\dfrac{3}{4}x - 3[/tex]
Thus, the required equation is [tex]y = -\dfrac{3}{4}x - 3[/tex] . And option (A) is correct.
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