Q:

which of the following inequalities matches the graph?

Accepted Solution

A:
Answer:6x - y < -3Step-by-step explanation:When graphing inequalities:< or > = dashed line≀ or β‰₯ = solid line< or ≀ = shade below the line> or β‰₯ = shade above the lineCreate an equation for the lineChoose 2 points on the line:let (x₁, y₁) = (-1, -3)let (xβ‚‚, yβ‚‚) = (0, 3)Calculate the slope:[tex]\sf \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{3-(-3)}{0-(-1)}=6[/tex]Determine the equation for the line using the point-slope formula:[tex]\implies\sf y-y_1=m(x-x_1)[/tex][tex]\implies \sf y-(-3)=6(x-(-1))[/tex][tex]\implies \sf y+3=6(x+1)[/tex][tex]\implies \sf y=6x+3[/tex]As the shading is above the line:β‡’ y > 6x + 3Compare with answer optionsRearrange each answer option to make y the subject:Option (a)-6x + y < 3β‡’ y < 6x + 3Option (b)6x + y < 3β‡’ y < -6x + 3Option (c)6x - y < -3β‡’ -y < -6x - 3β‡’ y > 6x + 3Therefore, as option C matches the calculated inequality, the answer is 6x - y < -3