Question

In the graph of an inequality, the region to the left of a dashed vertical linethrough the points (-3, 0) and (-3 ,5) are shaded. What inequality does the graphrepresent? Draw a graph if needed.

Answer 1

$x<-3$

Explanation

Step 1

find the equation of the line that passes through the points (-3, 0) and (-3 ,5)

a) find the slope of the line

the slope of a line is given by:

$\begin{gathered} \text{slope}=\frac{\text{ changeiny}}{\text{changein x}}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ \text{and} \\ P2(x_2,y_2) \\ \text{are 2 well known points from the line} \end{gathered}$

then, Let

P1(-3,0)

P2(-3,5)

replace

$\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ slope=\frac{5-0}{-3-(-3)}=\frac{5}{0}=\text{indefined}\Rightarrow vertical\text{ line} \end{gathered}$

therefore, the line is a vertical line

Step 2

now, to find the point where the line intersects the x-axis, check the x coomponent of any coordinate of the line,

so

$(-3,0)\Rightarrow-3$

we need to draw a dashed vertical line that passes through and then, shaded the left zone, so

Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region

therefore, the dashed zone represents all the x values smaller than -3

$x<-3$

I hope this helps you