In Exercises 63–64, write each sentence as an inequality in two v...

Question

In Exercises 63–64, write each sentence as an inequality in two variables. Then graph the inequality. The y-variable is at least 4 more than the product of -2 and the x-variable.

Accepted Answer

Hey, everyone here we are asked to convert the following statement into a system of inequality in two variables and graph the system. So here our given statement is the Y variable is at least nine more than the product of negative six. And the X variable here we have four answer choice options. First answer choice A where we have a graph with a solid line that passes through the points 09 and 1.5 and zero. And the area to the left of the line is shaded in. Then we have answer choice B which also is a solid line that passes through the points negative 1.5 and zero in the 00.0 and positive nine. And the area to the right of the line is shaded. Then we have answer choice C which is also a solid line that passes through the points 09 and 1.5 and zero. And the area to the right of the line is shaded. And lastly, we have answer choice D where we simply have no solution. So looking back at our given statement, which was the Y variable is at least nine more than the product of negative six and the X variable, we just want to begin by writing in inequality to describe this statement. So here we can begin by breaking up this statement. So we first have the Y variable is at least. So that tells us that Y is at least or greater than, or equal to nine, more than the product of. So we have nine plus the product of negative six and the X variables we have plus negative six times X. And now just rewriting our inequality is Y is greater than, or equal to nine minus six X. So now to solve this problem or find our appropriate graph, we can begin by graphing the equation rather than the inequality. So we can just graph Y is equal to nine minus six X. So graphing this line, we get a line that is decreasing and passes through the points 09 and 1.5 and zero. And we have a solid line again passing through these points. And now we want to include the inequality symbol. So if we recall, we have actually Y is greater than, or equal to nine minus six X. So now graphing with the inequality, we have the right side of the line shaded in because our greater than symbol is included here. And then the equals to symbol in the inequality gives us a solid line. So we have a solid line passing through the same points with the right side of the line shaded in. And so now with our finalized graph with the shaded region included, we see that our solution includes the line with the shaded region. And so we are left here with answer choice. C thanks for watching. I hope you found this video helpful and I'll see you again next time.

In Exercises 63–64, write each sentence as an inequality in two variables. Then graph the inequality. The y-variable is at least 4 more than the product of -2 and the x-variable.

Key Concepts

Inequalities in Two Variables

Graphing Inequalities

Translating Verbal Statements to Mathematical Expressions

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