3.4E: Exercises

Last updated
Save as PDF

Page ID: 110473

$ \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $ $ \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} $$\newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\kernel}{\mathrm{null}\,}$ $ \newcommand{\range}{\mathrm{range}\,}$ $ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$ $ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$ $ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$ $ \newcommand{\Span}{\mathrm{span}}$ $\newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\kernel}{\mathrm{null}\,}$ $ \newcommand{\range}{\mathrm{range}\,}$ $ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$ $ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$ $ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$ $ \newcommand{\Span}{\mathrm{span}}$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$

Practice Makes Perfect

Find the Equation Given a Slope and y-Intercept

In the following exercises, find the equation of a line with given slope and y-intercept. Write the equation in slope–intercept form.

Slope $\frac{1}{3}$ and $y$-intercept $(0,−6)$
Slope $−5$ and $y$-intercept $(0,−3)$
Slope $0$ and $y$-intercept $(0,4)$
Slope $−2$ and $y$-intercept $(0,0)$

Answer

$y=\frac{1}{3}-6$
$y=-5x-3$
$y=4$
$y=-2x$

Find the Equation Given a Graph

In the following exercises, find the equation of the line shown in each graph. Write the equation in slope–intercept form.

$This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 1), (1, 3), and (2, 5).$
$This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 5), (1, 2), and (2, negative 1).$
$This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 2), (4, 1), and (8, 4).$
$This figure has a graph of a horizontal straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 4), (1, negative 4), and (2, negative 4).$

Answer

$y=2x+1$
$y=-3x+5$
$y=\frac{3}{4}x-2$
$y=-4$

Find the Equation Given a Slope and a Point

In the following exercises, find the equation of a line with given slope and containing the given point. Write the equation in slope–intercept form.

$m=−\frac{1}{4}$, point $(−8,3)$
$m=\frac{3}{5}$, point $(10,6)$
Horizontal line containing $(−2,7)$
$m=−2$, point $(−1,−3)$

Answer

$y=-\frac{1}{4}x+1$
$y=\frac{3}{5}x$
$y=7$
$y=-2x-5$

Find the Equation Given Two Points

In the following exercises, find the equation of a line containing the given points. Write the equation in slope–intercept form.

$(2,10)$ and $(−2,−2)$
$(7,1)$ and $(5,0)$
$(3,8)$ and $(3,−4)$
$(5,2)$ and $(−1,2)$

Answer

$y=3x+4$
$y=\frac{1}{2}x-\frac{5}{2}$
$x=3$
$y=2$