Answer:
[tex]y<-\dfrac{1}{4} x+1\\OR\\ 4y<-x+4[/tex]
Step-by-step explanation:
First of all, let us try to find out the equation.
We can easily observe from the graph the values of x and y intercept.
x intercept is the value where y coordinate is 0.
We can see that y is 0 at x = 4
So, x intercept (4, 0)
y intercept is the value where x coordinate is 0.
We can see that y is 1 at x = 0
So, x intercept (0, 1)
Now, we have 2 points for the equation of line.
Slope intercept form:
[tex]y=mx+c[/tex]
Slope of a line:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]x_1 = 0\\x_2 = 4\\y_1 = 1\\y_2 = 0[/tex]
[tex]m=\dfrac{0-1}{4-0}\\\Rightarrow m =-\dfrac{1}{4 }[/tex]
[tex]y=-\dfrac{1}{4} x+c[/tex]
Putting the point (0, 1):
[tex]1=-\dfrac{1}{4} \times 0+c\\\Rightarrow c = 0[/tex]
So, the equation becomes:
[tex]y=-\dfrac{1}{4} x+1[/tex]
Let us try to put a point (0, 0) in the equation.
LHS becomes 0.
RHS becomes 1.
LHS < RHS (Only less than sign used because the line is dashed not solid)
So, the inequality is:
[tex]y<-\dfrac{1}{4} x+1\\OR\\ 4y<-x+4[/tex]
