Chapter 3

What is the rectangular coordinate system?

Use a graphing utility to graph each equation. You will need to solve the equation for \(y\) before entering it. Use the graph displayed on the screen to identify the \(x\)-intercept and the \(y\)-intercept. \(2 x+3 y=30\)

Explain how to plot a point in the rectangular coordinate system. Give an example with your explanation.

Use a graphing utility to graph each equation. You will need to solve the equation for \(y\) before entering it. Use the graph displayed on the screen to identify the \(x\)-intercept and the \(y\)-intercept. \(4 x-2 y=-40\)

Explain why \((5,-2)\) and \((-2,5)\) do not represent the same point.

Find the absolute value: \(|-13.4|\)

Explain how to find the coordinates of a point in the rectangular coordinate system.

Simplify: \(\quad 7 x-(3 x-5)\)

How do you determine whether an ordered pair is a solution of an equation in two variables, \(x\) and \(y ?\)

Solve: \(\quad 8(x-2)-2(x-3) \leq 8 x\).

Explain how to find ordered pairs that are solutions of an equation in two variables, \(x\) and \(y\)

Will help you prepare for the material covered in the next section. In each exercise, evaluate $$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$ for the given ordered pairs \(\left(x_{1}, y_{1}\right)\) and \(\left(x_{2}, y_{2}\right)\). \(\left(x_{1}, y_{1}\right)=(1,3) ;\left(x_{2}, y_{2}\right)=(6,13)\)

What is the graph of an equation?

Will help you prepare for the material covered in the next section. In each exercise, evaluate $$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$ for the given ordered pairs \(\left(x_{1}, y_{1}\right)\) and \(\left(x_{2}, y_{2}\right)\). \(\left(x_{1}, y_{1}\right)=(4,-2) ;\left(x_{2}, y_{2}\right)=(6,-4)\)

Explain how to graph an cquation in two variables in the rectangular coordinate system.

Will help you prepare for the material covered in the next section. In each exercise, evaluate $$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$ for the given ordered pairs \(\left(x_{1}, y_{1}\right)\) and \(\left(x_{2}, y_{2}\right)\). \(\left(x_{1}, y_{1}\right)=(3,4) ;\left(x_{2}, y_{2}\right)=(5,4)\)

determine whether each statement “makes sense” or “does not make sense” and explain your reasoning. When I know that an equation's graph is a straight line, I don't need to plot more than two points, although I sometimes plot three just to check that the points line up.

determine whether each statement “makes sense” or “does not make sense” and explain your reasoning. The graph that I'm looking at is U-shaped, so its equation cannot be of the form \(y=m x+b\)

determine whether each statement “makes sense” or “does not make sense” and explain your reasoning. I'm working with a linear equation in two variables and found that \((-2,2),(0,0),\) and \((2,2)\) are solutions.

I'm working with a linear equation in two variables and found that \((-2,2),(0,0),\) and \((2,2)\) are solutions. When a real-world situation is modeled with a linear cquation in two variables, I can use its graph to predict specific information about the situation.

determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The graph of any equation in the form \(y=m x+b\) passes through the point \((0, b)\)

determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The ordered pair \((3,4)\) satisfies the equation $$ 2 y-3 x=-6 $$

a. Graph each of the following points: $$ \left(1, \frac{1}{2}\right),(2,1),\left(3, \frac{3}{2}\right),(4,2) $$ Parts (b)-(d) can be answered by changing the sign of one or both coordinates of the points in part (a). b. What must be done to the coordinates so that the resulting graph is a mirror-image reflection about the \(y\) -axis of your graph in part (a)? c. What must be done to the coordinates so that the resulting graph is a mirror-image reflection about the \(x\) -axis of your graph in part (a)? d. What must be done to the coordinates so that the resulting graph is a straight-line extension of your graph in part (a)?

Use a graphing utility to graph in a standard viewing rectangle, \([-10,10,1]\) by \([-10,10,1]\). Then use the \([\text { TRACE }]\) feature to trace along the line and find the coordinates of two points. $$y=2 x-1$$

Use a graphing utility to graph in a standard viewing rectangle, \([-10,10,1]\) by \([-10,10,1]\). Then use the \([\text { TRACE }]\) feature to trace along the line and find the coordinates of two points. $$y=-3 x+2$$

Use a graphing utility to graph in a standard viewing rectangle, \([-10,10,1]\) by \([-10,10,1]\). Then use the \([\text { TRACE }]\) feature to trace along the line and find the coordinates of two points. $$y=\frac{1}{2} x$$

Use a graphing utility to graph in a standard viewing rectangle, \([-10,10,1]\) by \([-10,10,1]\). Then use the \([\text { TRACE }]\) feature to trace along the line and find the coordinates of two points. $$y=\frac{3}{4} x-2$$

$$\text { Solve: } 3 x+5=4(2 x-3)+7$$

$$\text { Simplify: } 3(1-2 \cdot 5)-(-28)$$

Solve for \(h: \quad V=\frac{1}{3} A h .\) (Section 2.4, Example 4)

will help you prepare for the material covered in the next section. Remember that a solution of an equation in two variables is an ordered pair. Let \(y=0\) and find a solution of \(3 x-4 y=24\)

will help you prepare for the material covered in the next section. Remember that a solution of an equation in two variables is an ordered pair. Let \(x=0\) and find a solution of \(3 x-4 y=24\)

will help you prepare for the material covered in the next section. Remember that a solution of an equation in two variables is an ordered pair. Let \(x=0\) and find a solution of \(x+2 y=0\)