Question

Which system of linear inequalities Is represented by this graphed solution?

Answer 1

Answer:

y ≥ 3x - 1

y < $-\frac{1}{2}x+2$

Step-by-step explanation:

Let the equation of the solid line passing through (x', y') given in graph is,

y = mx + b

Here m = slope of the line

b = y-intercept

Slope of the solid line =

                                 m = $\frac{3}{1}$

                                 m = 3

y - intercept 'b' = -1

Therefore, equation of the line will be,

y = 3x - 1

Since, shaded (blue) area is above the line, inequality that will represent the solution area will be,

y ≥ 3x - 1

For the dotted line,

Slope of the line (m) = $\frac{\text{Rise}}{\text{Run}}$

                                  = $\frac{-2}{4}$

                                  = $-\frac{1}{2}$

y-intercept (b) = 2

Equation of the dotted line → y = $-\frac{1}{2}x+2$

Since, shaded (grey color) area is below the dotted line,

Inequality representing the solution area will be,

y < $-\frac{1}{2}x+2$