Question

Write the inequality for the graph below. In two or three sentences, explain how you generated the inequality. Make sure to explain how you got the slope, y-intercept, and inequality.

Answer 1

`y<-(1)/(4) x+1\\OR\\ 4y<-x+4`

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:

`y=mx+c`

Slope of a line:

`m=(y_2-y_1)/(x_2-x_1)`

`x_1 = 0\\x_2 = 4\\y_1 = 1\\y_2 = 0`

`m=(0-1)/(4-0)\\\Rightarrow m =-(1)/(4 )`

`y=-(1)/(4) x+c`

Putting the point (0, 1):

`1=-(1)/(4) * 0+c\\\Rightarrow c = 0`

So, the equation becomes:

`y=-(1)/(4) x+1`

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:

`y<-(1)/(4) x+1\\OR\\ 4y<-x+4`