Question

Find a linear inequality with the following solution set. Each grid line represents one unit.

Answer 1

Answer:

-0.5x + y + 0.5 > 0

Step-by-step explanation:

Let the equation of the line is,

y - y' = m(x - x')

where (x', y') is a point lying on the line

m = slope of the line

Since two points (1, 0) and (3, 1) lie on the line,

Therefore, slope of the line 'm' = $\frac{y_2-y_1}{x_2-x_1}$

m = $\frac{1-0}{3-1}$

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

Equation of line passing through (1, 0) and slope = $\frac{1}{2}$ will be,

y - 0 = $\frac{1}{2}(x-1)$

y = 0.5x - 0.5

Since, line given in the graph is a dotted line therefore, its an inequality having sign of (> or <).

In this inequality shaded region is above the dotted line therefore, inequality representing the solutions by the shaded region will be,

y > 0.5x - 0.5

-0.5x + y + 0.5 > 0