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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.

1 Answer

1 vote


x<-3Step-by-step 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}}=(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}=(y_2-y_1)/(x_2-x_1) \\ slope=(5-0)/(-3-(-3))=(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

In the graph of an inequality, the region to the left of a dashed vertical linethrough-example-1
User Shumin
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