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Chapter 7: Problem 14

Plot the given point in a rectangular coordinate system. \(\left(-3,-1 \frac{1}{2}\right)\)

Short Answer

Expert verified
The point \(-3, -1 \frac{1}{2}\) is plotted 3 units to the left of the origin on the x-axis and \(\frac{3}{2}\) units below the origin on the y-axis.

Step by step solution

01

Understand the coordinate system

A rectangular coordinate system consists of two perpendicular lines: a horizontal x-axis and a vertical y-axis. They intersect at a point called the origin, notated as (0, 0). Movements to the right are positive and to the left are negative on the x-axis. Movements upwards are positive and downwards are negative on the y-axis.
02

Plot the x-coordinate

The given point has an x-coordinate of -3. Start at the origin (0,0). Move 3 units to the left along the x-axis since the value is negative.
03

Plot the y-coordinate

The given point has a y-coordinate of \(-1 \frac{1}{2}\). From the point arrived at in Step 2, move \(\frac{1}{2}\) units downwards along the y-axis since the value is negative.
04

Mark the final coordinate point

The point at which you've arrived, is the point \(-3, -1 \frac{1}{2}\). Mark this point on the graph.

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Most popular questions from this chapter

Write each sentence as an inequality in two variables. Then graph the inequality. The \(y\)-variable is at least 2 more than the product of \(-3\) and the \(x\)-variable.

a. Determine if the parabola whose equation is given opens upward or downward. b. Find the vertex. c. Find the \(x\)-intercepts. d. Find the \(y\)-intercept. e. Use (a)-(d) to graph the quadratic function. \(f(x)=x^{2}+4 x-5\)

The graphs of solution sets of systems of inequalities involve finding the intersection of the solution sets of two or more inequalities. By contrast, in Exercises 43-44, you will be graphing the union of the solution sets of two inequalities. Graph the union of \(y>\frac{3}{2} x-2\) and \(y<4\).

Graph each linear inequality. \(y \leq 2 x-1\)

Graph the solution set of each system of inequalities. \(\left\\{\begin{array}{r}2 x+y<3 \\ x-y>2\end{array}\right.\)
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