Answer:
The inequality is y > 1/2 x - 2
Explanation:
* To solve this problem we must to know how to make an equation
of the line from two point
- If the line passes through points (x1 , y1) and (x2 , y2)
- The form of the equation is y = mx + c, where m is the slope of the
line and c is the y-intercept
- The rule of the slope is m = (y2 - y1)/(x2 - x1)
- The y-intercept means the line intersect the y-axis at point (0 ,c)
* Now lets solve the problem
- To write the inequality we must to make the equation of the line
from any two points on it
∵ The line passes through points (4 , 0) and (0 , -2)
- Let (4 , 0) is (x1 , y1) and (0 , -2) is (x2 , y2)
∵ m = (y2 - y1)/(x2 - x1)
∴ m = (-2 - 0)/(0 - 4)
∴ m = (-2)/-4 = 1/2
- Lets write the form of the equation
∵ y = mx + c ⇒ substitute the value of m
∴ y = 1/2 x + c
- The line intersects the y-axis at point (0 , -2)
∴ c = -2
∴ y = 1/2 x + -2
∴ y = 1/2 x - 2
- lets look to the line if it is dashed line then there is no equal with the
inequality (> , <) sign, if it is solid line then there is equal with the
inequality sign (≥ , ≤)
∵ The line is dashed line
∴ The sign of inequality is > or <
- Lets look to the shaded part, if it is over the line then the inequality
will be y > 1/2 x - 2, if it is under the line then the inequality will
be y < 1/2 x - 2
∵ The shaded part is over the line
∴ y > 1/2 x - 2
* The inequality is y > 1/2 x - 2