Lynn Marecek; MaryAnne Anthony-Smith

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 the following exercises, for each ordered pair, decide

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

295.

$y = - x + 4$

ⓐ $(0, 4)$
ⓑ $(−1, 3)$
ⓒ $(2, 2)$
ⓓ $(−2, 6)$

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”.

296.

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

ⓐ $(0, −1)$
ⓑ $(3, 1)$
ⓒ $(−3, −3)$
ⓓ $(6, 4)$

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

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.

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.

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?