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

Answer:

$y$

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:

$y=mx+c$

Slope of a line:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

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

$m=\dfrac{0-1}{4-0}\\\Rightarrow m =-\dfrac{1}{4 }$

$y=-\dfrac{1}{4} x+c$

Putting the point (0, 1):

$1=-\dfrac{1}{4} \times 0+c\\\Rightarrow c = 0$

So, the equation becomes:

$y=-\dfrac{1}{4} x+1$

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:

$y$