11.7.1: Review Exercises

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May 28, 2023
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- 11.7: Exercises
- 11.7.2: Practice Test

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Review Exercises

Use the Rectangular Coordinate System

Plot Points in a Rectangular Coordinate System

In the following exercises, plot each point in a rectangular coordinate system.

277.

$(1, 3), (3, 1)$

278.

$(2, 5), (5, 2)$

In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.

279.

ⓐ $(−1, −5)$
ⓑ $(−3, 4)$
ⓒ $(2, −3)$
ⓓ $(1, \frac{5}{2})$

280.

ⓐ $(3, −2)$
ⓑ $(−4, −1)$
ⓒ $(−5, 4)$
ⓓ $(2, \frac{10}{3})$

Identify Points on a Graph

In the following exercises, name the ordered pair of each point shown in the rectangular coordinate system.

281.

$The graph shows the x y-coordinate plane. The axes run from -7 to 7. “a” is plotted at 5, 3, “b” at 2, -1, “c” at -3,-2, and “d” at -1,4.$

282.

$The graph shows the x y-coordinate plane. The axes run from -7 to 7. “a” is plotted at -2, 2, “b” at 3, 5, “c” at 4,-1, and “d” at -1,3.$

283.

$The graph shows the x y-coordinate plane. The axes run from -7 to 7. “a” is plotted at 2, 0, “b” at 0, -5, “c” at -4,0, and “d” at 0,3.$

284.

$The graph shows the x y-coordinate plane. The axes run from -7 to 7. “a” is plotted at 0, 4, “b” at 5, 0, “c” at 0,-1, and “d” at -3,0.$

Verify Solutions to an Equation in Two Variables

In the following exercises, find the ordered pairs that are solutions to the given equation.

285.

$5 x + y = 10$

ⓐ $(5, 1)$
ⓑ $(2, 0)$
ⓒ $(4, −10)$

286.

$y = 6 x - 2$

ⓐ $(1, 4)$
ⓑ $(\frac{1}{3}, 0)$
ⓒ $(6, −2)$

Complete a Table of Solutions to a Linear Equation in Two Variables

In the following exercises, complete the table to find solutions to each linear equation.

287.

$y = 4 x - 1$

$x$	$y$	$(x, y)$
$0$
$1$
$−2$

288.

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

$x$	$y$	$(x, y)$
$0$
$1$
$−2$

289.

$x + 2 y = 5$

$x$	$y$	$(x, y)$
	$0$
$1$
$−1$

290.

$3 x - 2 y = 6$

$x$	$y$	$(x, y)$
$0$
	$0$
$−2$

Find Solutions to a Linear Equation in Two Variables

In the following exercises, find three solutions to each linear equation.

291.

$x + y = 3$

292.

$x + y = −4$

293.

$y = 3 x + 1$

294.

$y = - x - 1$

Graphing Linear Equations

Recognize the Relation Between the Solutions of an Equation and its Graph

In each of the following exercises, an equation and its graph is shown. For each ordered pair, decide

ⓐ if the ordered pair is a solution to the equation.
ⓑ if the point is on the line.

295.

$y = - x + 4$

$The graph shows the x y-coordinate plane. The axes run from -7 to 7. A line passes through the points “ordered pair 0, 4” and “ordered pair 4, 0”.$

$(0, 4)$
$(−1, 3)$
$(2, 2)$
$(−2, 6)$

296.

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

$The graph shows the x y-coordinate plane. The axes run from -7 to 7. A line passes through the points “ordered pair 0, -1” and “ordered pair 3, 1”.$

$(0, −1)$
$(3, 1)$
$(−3, −3)$
$(6, 4)$

Graph a Linear Equation by Plotting Points

In the following exercises, graph by plotting points.

297.

$y = 4 x - 3$

298.

$y = −3 x$

299.

$2 x + y = 7$

Graph Vertical and Horizontal lines

In the following exercises, graph the vertical or horizontal lines.

300.

$y = −2$

301.

$x = 3$

Graphing with Intercepts

Identify the Intercepts on a Graph

In the following exercises, find the $x -$ and $y -intercepts .$

302.

$The graph shows the x y-coordinate plane. The axes run from -7 to 7. A line passes through the points “ordered pair 0, 4” and “ordered pair -4, 0”.$

303.

$The graph shows the x y-coordinate plane. The x-axis runs from -1 to 6. The y-axis runs from -4 to 2. A line passes through the points “ordered pair 5, 1” and “ordered pair 0, -3”.$

Find the Intercepts from an Equation of a Line

In the following exercises, find the intercepts.

304.

$x + y = 5$

305.

$x - y = −1$

306.

$y = \frac{3}{4} x - 12$

307.

$y = 3 x$

Graph a Line Using the Intercepts

In the following exercises, graph using the intercepts.

308.

$- x + 3 y = 3$

309.

$x + y = −2$

Choose the Most Convenient Method to Graph a Line

In the following exercises, identify the most convenient method to graph each line.

310.

$x = 5$

311.

$y = −3$

312.

$2 x + y = 5$

313.

$x - y = 2$

314.

$y = \frac{1}{2} x + 2$

315.

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

Understand Slope of a Line

Use Geoboards to Model Slope

In the following exercises, find the slope modeled on each geoboard.

316.

$The figure shows a grid of evenly spaced dots. There are 5 rows and 5 columns. There is a rubber band style loop connecting the point in column 1 row 4 and the point in column 4 row 2.$

317.

$The figure shows a grid of evenly spaced dots. There are 5 rows and 5 columns. There is a rubber band style loop connecting the point in column 1 row 5 and the point in column 4 row 1.$

318.

$The figure shows a grid of evenly spaced dots. There are 5 rows and 5 columns. There is a rubber band style loop connecting the point in column 1 row 3 and the point in column 4 row 4.$

319.

$The figure shows a grid of evenly spaced dots. There are 5 rows and 5 columns. There is a rubber band style loop connecting the point in column 1 row 2 and the point in column 4 row 4.$

In the following exercises, model each slope. Draw a picture to show your results.

320.

$\frac{1}{3}$

321.

$\frac{3}{2}$

322.

$- \frac{2}{3}$

323.

$- \frac{1}{2}$

Find the Slope of a Line from its Graph

In the following exercises, find the slope of each line shown.

324.

$The graph shows the x y-coordinate plane. The axes run from -7 to 7. A line passes through the points “ordered pair 0, 0” and “ordered pair 2, -6”.$

325.

$The graph shows the x y-coordinate plane. The axes run from -7 to 7. A line passes through the points “ordered pair 0, 4” and “ordered pair -4, 0”.$

326.

$The graph shows the x y-coordinate plane. The axes run from -7 to 7. A line passes through the points “ordered pair -4, -4” and “ordered pair 5, -1”.$

327.

$The graph shows the x y-coordinate plane. The axes run from -7 to 7. A line passes through the points “ordered pair -3, 6” and “ordered pair 5, 2”.$

Find the Slope of Horizontal and Vertical Lines

In the following exercises, find the slope of each line.

328.

$y = 2$

329.

$x = 5$

330.

$x = −3$

331.

$y = −1$

Use the Slope Formula to find the Slope of a Line between Two Points

In the following exercises, use the slope formula to find the slope of the line between each pair of points.

332.

$(2, 1), (4, 5)$

333.

$(−1, −1), (0, −5)$

334.

$(3, 5), (4, −1)$

335.

$(−5, −2), (3, 2)$

Graph a Line Given a Point and the Slope

In the following exercises, graph the line given a point and the slope.

336.

$(2, −2); m = \frac{5}{2}$

337.

$(−3, 4); m = - \frac{1}{3}$

Solve Slope Applications

In the following exercise, solve the slope application.

338.

A roof has rise $10$ feet and run $15$ feet. What is its slope?

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Review Exercises

Use the Rectangular Coordinate System

Review Exercises

Use the Rectangular Coordinate System

Graphing Linear Equations

Graphing with Intercepts

Understand Slope of a Line

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