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nikdorinn [45]
3 years ago
13

Help solve 87 please

Mathematics
1 answer:
RSB [31]3 years ago
7 0

Answer:

The inequality is y > 1/2 x - 2

Step-by-step 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

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