Question

I need help graphing this chart for my homework please

Answer 1

Step-by-step explanation:

Here, we want to graph the inequality

To graph the inequality, we will draw the line like would normally do then shade a part of the graph according to the inequality sign

The general equation of a straight line is:

`y\text{ = mx + b}`

where m is the slope of the graph and b is the y-intercept

To graph the line, we need the x-intercept and the y-intercept

Rearranging the given inequality, we have it that:

`\begin{gathered} x-1\text{ > 2y} \\ 2y\text{ < x - 1} \\ y\text{ < }(x)/(2)-(1)/(2) \end{gathered}`

The y-intercept is the point (0,-1/2)

For the x-intercept, we set y = 0:

`\begin{gathered} 0\text{ < }(x)/(2)-(1)/(2) \\ (1)/(2)<(x)/(2) \\ \\ 1\text{ < x} \end{gathered}`

The x-interecpt is (1,0)

We join the points (1,0) and (0,-1/2) with broken lines since the inequality has no equality sign attached to it

For the second inequality, we simply draw a horizontal line that passes through the point y=2 or (0,2)

Now, let us combine the two inequalities:

The shaded portion simply starts from the point at which the two lines intersect which is the point (5,2) and extend to every part between the two lines only