3.2E: Exercises

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Practice Makes Perfect

Graph by Plotting Points

In the following exercises, graph by plotting points.

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

Answer

$This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The line goes through the points (negative 3, negative 1), (negative 2, 0), (negative 1, 1), (0, 2), (1, 3), (2, 4), and (3, 5).$
$This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The line goes through the points (negative 3, negative 10), (negative 2, negative 7), (negative 1, negative 4), (0, negative 1), (1, 2), (2, 5), (3, 8), and (4, 11).$
$This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The line goes through the points (negative 3, 0), (negative 2, negative 1), (negative 1, negative 2), (0, negative 3), (1, negative 4), (2, negative 5), (3, negative 6), and (4, negative 7).$
$This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The line goes through the points (negative 3, negative 6), (negative 2, negative 4), (negative 1, negative 2), (0, 0), (1, 2), (2, 4), and (3, 6).$
$This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The line goes through the points (negative 6, negative 2), (negative 4, 0), (negative 2, 1), (0, 2), (2, 3), (4, 4), and (6, 5).$

Graph Vertical and Horizontal lines.

In the following exercises, graph each equation.

$x=4$
$y=3$
$x=−2$
$y=−5$

Answer

$This figure shows a vertical straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The line goes through the points (4, negative 1), (4, 0), and (4, 1).$
$This figure shows a horizontal straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The line goes through the points (negative 1, 3), (0, 3), and (1, 3).$
$This figure shows a vertical straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The line goes through the points (negative 2, negative 1), (negative 2, 0), and (negative 2, 1).$
$This figure shows a horizontal straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 12 to 12. The line goes through the points (negative 1, negative 5), (0, negative 5), and (1, negative 5).$

Graph Each Pair of Equations

In the following exercises, graph each pair of equations in the same rectangular coordinate system.

$y=2x$ and $y=2$
$y=−\frac{1}{2}x$ and $y=−\frac{1}{2}$

Answer

$The figure shows the graphs of a straight horizontal line and a straight slanted line on the same x y-coordinate plane. The x and y axes run from negative 12 to 12. The horizontal line goes through the points (0, 2), (1, 2), and (2, 2). The slanted line goes through the points (0, 0), (1, 2), and (2, 4).$
$The figure shows the graphs of a straight horizontal line and a straight slanted line on the same x y-coordinate plane. The x and y axes run from negative 12 to 12. The horizontal line goes through the points (0, negative 1 divided 2), (1, negative 1 divided 2), and (2, negative 1 divided 2). The slanted line goes through the points (0, 0), (1, negative 1 divided 2), and (2, negative 1).$

Find x- and y-intercepts From a Graph

In the following exercises, find the x- and y-intercepts on each graph.

$The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 6, 9), (negative 3, 6), (0, 3), (3, 0), and (6, negative 3).$
$The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 1, negative 6), (0, negative 5), (2, negative 3), (5, 0), and (7, 2).$

Answer

$(3,0),(0,3)$
$(5,0),(0,−5)$

Find Intercepts for Equations

In the following exercises, find the intercepts for each equation.

$x−y=5$
$3x+y=6$
$4x−y=8$
$2x+5y=10$

Answer

$x$-int: $(5,0)$, $y$-int: $(0,−5)$
$x$-int: $(2,0)$, $y$-int: $(0,6)$
$x$-int: $(2,0)$, $y$-int: $(0,−8)$
$x$-int: $(5,0)$, $y$-int: $(0,2)$

Graph using Intercepts

In the following exercises, graph using the intercepts.

$−x+4y=8$
$x+y=−3$
$4x+y=4$
$3x−y=−6$
$2x+4y=12$

Answer

$The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 12 to 12. The line goes through the points (negative 8, 0), (0, 2), (4, 3), and (8, 4).$
$The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 12 to 12. The line goes through the points (negative 3, 0), (0, negative 3), and (3, negative 6).$
$The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 12 to 12. The line goes through the points (0, 4), (1, 0), and (2, negative 4).$
$The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 12 to 12. The line goes through the points (negative 2, 0), (negative 1, 3), and (0, 6).$
$The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (0, 3), (2, 2), and (6, 0).$