Question

Write the inequality of the following graph

Answer 1

We can notice that : Line Passes through the Points (0 , 3) and (1 , 0)

Let us find the slope of the line in order to write the Equation of the Line.

Slope of a Line Passing through two points (x₁ , y₁) and (x₂ , y₂) is given by :

`\heartsuit\; Slope(m) = (y_1 - y_2)/(x_1 - x_2)`

Points are (0 , 3) and (1 , 0)

here x₁ = 0 and x₂ = 1 and y₁ = 3 and y₂ = 0

`\heartsuit\; Slope(m) = (3 - 0)/(0 - 1) = (3)/(-1) = -3`

As the line passes through (0 , 3) , The y - intercept is 3

We know that Equation of line is given by : y = mx + c

where m is the slope and c is the y-intercept

here m = -3 and c = 3

Equation of the Given line : y = -3x + 3

⇒ -3x - y = -3

⇒ 3x + y = 3

As the Given line is a Dotted line and the Shaded Region is Towards the Origin

The Inequality of the Graph is : 3x + y < 3