Chapter 3

What does it mean to say that b is a function of a?

After reading this section, write out the answers to these questions. Use complete sentences. What is the point called at the intersection of the \(x\) -and \(y\) -axis?

After reading this section, write out the answers to these questions. Use complete sentences. What is an ordered pair?

Why does a horizontal line have zero slope?

Why is slope undefined for vertical lines?

What is the relationship between the slopes of perpendicular lines?

What is the relationship between the slopes of parallel lines?

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies. $$(2,5)$$

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies. $$(-5,1)$$

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies. $$\left(-3,-\frac{1}{2}\right)$$

In each situation determine whether \(y\) is a function of \(x\). Explain your answer See Example I. Consider all students taking algebra at your school. Let \(x\) represent a student's height to the nearest inch and \(y\) represent the student's IQ.

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies. $$(-2,-6)$$

In each situation determine whether \(y\) is a function of \(x\). Explain your answer See Example I. Consider the air temperature at noon today in every town in the United States. Let \(x\) represent the Celsius temperature for a town and \(y\) represent the Fahrenheit temperature.

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies. $$(0,4)$$

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies. $$(0,2)$$

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies. $$(\pi,-1)$$

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies. $$\left(\frac{4}{3}, 0\right)$$

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies. $$(-4,3)$$

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies. $$(0,-3)$$

Write a formula that describes the function. See Examples 2 and 3. The sales tax rate on groceries in Mayberry is \(9 \% .\) Express the total cost \(T\) (including tax) as a function of the total price of the groceries \(S\).

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies. $$\left(\frac{3}{2}, 0\right)$$

Write a formula that describes the function. See Examples 2 and 3. With a GM MasterCard, \(5 \%\) of the amount charged is credited toward a rebate on the purchase of a new car. Express the rebate \(R\) as a function of the amount charged \(A\).

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies. $$(3,2)$$

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies. $$\left(0,-\frac{7}{3}\right)$$

Find the slope of the line that contains each of the following pairs of points. \((2,6),(5,1)\)

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies. $$\left(4,-\frac{10}{3}\right)$$

Find the slope of the line that contains each of the following pairs of points. \((3,4),(6,10)\)

Write a formula that describes the function. See Examples 2 and 3. Express the perimeter \(P\) of a square as a function of the length \(s\) of a side.

Graph each linear equation. Plot four points for each line. $$y=x+1$$

Find the slope of the line that contains each of the following pairs of points. \((-3,-1),(4,3)\)a

Write a formula that describes the function. See Examples 2 and 3. Express the perimeter \(P\) of a rectangle with width 10 ft as a function of its length \(L\)

Graph each linear equation. Plot four points for each line. $$y=x-1$$

Graph each linear equation. Plot four points for each line. $$y=-2 x+3$$

Find the slope of the line that contains each of the following pairs of points. \((-2,2),(-1,7)\)

Graph each linear equation. Plot four points for each line. $$y=2 x-3$$

Find the slope of the line that contains each of the following pairs of points. \((-3,5),(1,-6)\)

Graph each linear equation. Plot four points for each line. $$y=x$$

Find the slope of the line that contains each of the following pairs of points. \((3,-5),(0,0)\)

Graph each linear equation. Plot four points for each line. $$y=-x$$

Find the slope of the line that contains each of the following pairs of points. \((0,0),(-2,-1)\)

Graph each linear equation. Plot four points for each line. $$y=3$$

Find the slope of the line that contains each of the following pairs of points. \((0,3),(5,0)\)

Graph each linear equation. Plot four points for each line. $$y=-2$$

Find the slope of the line that contains each of the following pairs of points. \((3,0),(0,10)\)

Graph each linear equation. Plot four points for each line. $$y=1-x$$

Find the slope of the line that contains each of the following pairs of points. \(\left(\frac{3}{4},-1\right),\left(-\frac{1}{2},-\frac{1}{2}\right)\)

Graph each linear equation. Plot four points for each line. $$y=2-x$$

Find the slope of the line that contains each of the following pairs of points. \(\left(\frac{1}{2}, 2\right),\left(\frac{1}{4}, \frac{1}{2}\right)\)

Graph each linear equation. Plot four points for each line. $$x=2$$

Find the slope of the line that contains each of the following pairs of points. \((6,212),(7,209)\)