Chapter 5

Explain the difference between linear interpolation and linear extrapolation.

Name the following form of the equation of a line: \(y=m x+b\).

Name the following form of the equation of a line: \(y-y_{1}=m\left(x-x_{1}\right)\)

The line that most closely fits a set of data is called the _____.

Compare writing linear equations given the slope and a point with writing linear equations given two points.

Two nonvertical lines that have the same slope must be \(\underline{?}\).

Is 5 the \(x\) -intercept or the \(y\) -intercept of the line \(y=3 x+5 ?\) Explain.

Explain how to decide whether a data set can be represented by a linear model.

Name the following form of the equation of a line: \(A x+B y=C\).

What are the values of \(m, x_{1},\) and \(y_{1}\) in the equation \(y-(-1)=3(x-2) ?\)

Explain why you should find the slope \(m\) first when finding the equation of a line passing through two points.

Explain how to find the equation of a line given its slope and a point on the line.

The equations \(y=-\frac{2}{3} x+3\) and \(2 x+3 y=9\) are equivalent. Describe how you would use each equation to graph the equation.

Give the slope of a line perpendicular to the given line. $$ y=-4 x+2 $$

Write an equation of the line that passes through the point and has the given slope. Write the equation in slope-intercept form. $$(3,4), m=\frac{1}{2}$$

Write an equation of the line in slope-intercept form. The slope is \(1 ;\) the \(y\) -intercept is \(0 .\)

Write the equation in standard form with integer coefficients. $$y=2 x-9$$

Give the slope of a line perpendicular to the given line. $$ y=\frac{1}{2} x-3 $$

Write an equation of the line that passes through the point and has the given slope. Write the equation in slope-intercept form. $$(2,-4), m=-5$$

Write an equation of the line in slope-intercept form. The slope is \(-7 ;\) the \(y\) -intercept is \(-\frac{2}{3}\)

Write the equation in standard form with integer coefficients. $$y=6-5 x$$

Give the slope of a line perpendicular to the given line. $$ y=x-3 $$

Write an equation of the line that passes through the point and has the given slope. Write the equation in slope-intercept form. $$(10,-10), m=\frac{2}{3}$$

Write an equation of the line in slope-intercept form. The slope is \(-1 ;\) the \(y\) -intercept is 3

Write the equation in standard form with integer coefficients. $$y=9+1 x$$

Use the data on bottled water consumption per person. $$ \begin{array}{|c|c|}\hline \text { Year } & \text { Water(in gallons) } \\\\\hline 1980 & 2.4 \\\\\hline 1985 & 4.5 \\\\\hline 1990 & 8.0 \\\\\hline 1995 & 11.6 \\\\\hline\end{array} $$ Make a scatter plot of the data.

Write an equation of the line in point-slope form that passes through the given point and has the given slope. $$ (2,-1), m=3 $$

Draw a scatter plot of the data. State whether x and y have a positive correlation, a negative correlation, or relatively no correlation. If possible, draw a line that closely fits the data and write an equation of the line. $$ \begin{array}{|c|c|} \hline x & y \\ \hline 1 & 2 \\ \hline 2 & 9 \\ \hline 3 & 8 \\ \hline 4 & 1 \\ \hline 5 & 4 \\ \hline 6 & 8 \\ \hline \end{array} $$

Write an equation of the line that passes through the point and has the given slope. Write the equation in slope-intercept form. $$(-12,2), m=-2$$

Write an equation of the line in slope-intercept form. The slope is \(-2 ;\) the \(y\) -intercept is \(0 .\)

Write the equation in standard form with integer coefficients. $$y=\frac{1}{2} x+8$$

Use the data on bottled water consumption per person. $$ \begin{array}{|c|c|}\hline \text { Year } & \text { Water(in gallons) } \\\\\hline 1980 & 2.4 \\\\\hline 1985 & 4.5 \\\\\hline 1990 & 8.0 \\\\\hline 1995 & 11.6 \\\\\hline\end{array} $$ Write a linear model for the data.

Write an equation of the line in point-slope form that passes through the given point and has the given slope. $$ (3,4), m=\frac{1}{2} $$

Draw a scatter plot of the data. State whether x and y have a positive correlation, a negative correlation, or relatively no correlation. If possible, draw a line that closely fits the data and write an equation of the line. $$ \begin{array}{|r|r|} \hline x & y \\ \hline-3 & 8 \\ \hline-2 & 6 \\ \hline-1 & 5 \\ \hline 0 & 3 \\ \hline 1 & 2 \\ \hline 2 & 0 \\ \hline \end{array} $$

Write an equation of the line that passes through the point and has the given slope. Write the equation in slope-intercept form. $$(4,8), m=5$$

Write an equation of the line in slope-intercept form. The slope is \(-3 ;\) the \(y\) -intercept is \(\frac{1}{2}\)

Write the equation in standard form with integer coefficients. $$y=7 x+3$$

Use the data on bottled water consumption per person. $$ \begin{array}{|c|c|}\hline \text { Year } & \text { Water(in gallons) } \\\\\hline 1980 & 2.4 \\\\\hline 1985 & 4.5 \\\\\hline 1990 & 8.0 \\\\\hline 1995 & 11.6 \\\\\hline\end{array} $$ Use your model to estimate the consumption of bottled water in the given year. Tell whether you use linear interpolation or linear extrapolation. $$ 1994 $$

Write an equation of the line in point-slope form that passes through the given point and has the given slope. $$ (-5,-7), m=-2 $$

Draw a scatter plot of the data. State whether x and y have a positive correlation, a negative correlation, or relatively no correlation. If possible, draw a line that closely fits the data and write an equation of the line. $$ \begin{array}{|c|c|} \hline x & y \\ \hline 1.1 & 5.1 \\ \hline 1.7 & 5.5 \\ \hline 2.2 & 5.9 \\ \hline 2.6 & 6.3 \\ \hline 3.3 & 7.5 \\ \hline 3.5 & 7.6 \\ \hline \end{array} $$

Write an equation of the line that passes through the point and has the given slope. Write the equation in slope-intercept form. $$(0,-5), m=0$$

Write an equation of the line in slope-intercept form. The slope is \(4 ;\) the \(y\) -intercept is \(-6\)

Write the equation in standard form with integer coefficients. $$y=-2+\frac{3}{2} x$$

Use the data on bottled water consumption per person. $$ \begin{array}{|c|c|}\hline \text { Year } & \text { Water(in gallons) } \\\\\hline 1980 & 2.4 \\\\\hline 1985 & 4.5 \\\\\hline 1990 & 8.0 \\\\\hline 1995 & 11.6 \\\\\hline\end{array} $$ Use your model to estimate the consumption of bottled water in the given year. Tell whether you use linear interpolation or linear extrapolation. $$ 2010 $$

Write an equation of the line in point-slope form that passes through the given point and has the given slope. $$ (-3,10), m=4 $$

Draw a scatter plot of the data. State whether x and y have a positive correlation, a negative correlation, or relatively no correlation. If possible, draw a line that closely fits the data and write an equation of the line. $$ \begin{array}{|c|c|} \hline x & y \\ \hline 5.5 & 0.4 \\ \hline 6.2 & 1.0 \\ \hline 7.7 & 2.5 \\ \hline 8.1 & 2.9 \\ \hline 9.2 & 4.3 \\ \hline 9.7 & 5.5 \\ \hline \end{array} $$

Write an equation in slope-intercept form of the line that passes through the points. $$ (-1,1),(4,5) $$

Write an equation of the line that is parallel to the given line and passes through the point. $$y=\frac{1}{2} x+8,(-6,4)$$

Suppose that bike rentals cost \(\$ 4\) plus \(\$ 1.50\) per hour. Write an equation to model the total cost \(y\) of renting a bike for \(x\) hours.

Write an equation in standard form of the line that passes through the given point and has the given slope. $$(-3,4), m=-4$$