40 Practice: Graphing and Slope (3.1 – 3.4) — Intermediate Algebra

3.1 Points and Coordinates

What are the coordinates of each point on the graph below?
Plot and label the following points on the graph.

$\begin{array}{lll} \text{A }(-5,5)&\text{B }(1,0)&\text{C }(-3,4) \\ \text{D }(-3,0)&\text{E }(-4, 2)&\text{F }(4,-2) \\ \text{G }(-2,-2)&\text{H }(3,-2)&\text{I }(0,3) \end{array}$

3.2 Midpoint and Distance Between Points

For questions 1 to 8, find the distance between the points.

(−6, −1) and (6, 4)
(1, −4) and (5, −1)
(−5, −1) and (3, 5)
(6, −4) and (12, 4)
(−8, −2) and (4, 3)
(3, −2) and (7, 1)
(−10, −6) and (−2, 0)
(8, −2) and (14, 6)

For questions 9 to 16, find the midpoint between the points.

(−6, −1) and (6, 5)
(1, −4) and (5, −2)
(−5, −1) and (3, 5)
(6, −4) and (12, 4)
(−8, −1) and (6, 7)
(1, −6) and (3, −2)
(−7, −1) and (3, 9)
(2, −2) and (12, 4)

3.3 Slopes and Their Graphs

For questions 1 to 6, find the slope of each line shown on the graph.

For questions 7 to 26, find the slope of the line that would connect each pair of points.

(2, 10), (−2, 15)
(1, 2), (−6, −12)
(−5, 10), (0, 0)
(2, −2), (7, 8)
(4, 6), (−8, −10)
(−3, 6), (9, −6)
(−2 −4), (10, −4)
(3, 5), (2, 0)
(−4, 4), (−6, 8)
(9, −6), (−7, −7)
(2, −9), (6, 4)
(−6, 2), (5, 0)
(−5, 0), (−5, 0)
(8, 11), (−3, −13)
(−7, 9), (1, −7)
(1, −2), (1, 7)
(7, −4), (−8, −9)
(−8, −5), (4, −3)
(−5, 7), (−8, 4)
(9, 5), (5, 1)

3.4 Graphing Linear Equations

For questions 1 to 10, sketch each linear equation using the slope-intercept method.

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

For questions 11 to 20, sketch each linear equation using the $x\text{-}$ and $y$ -intercepts.

$x + 4y = -4$
$2x - y = 2$
$2x + y = 4$
$3x + 4y = 12$
$2x - y = 2$
$4x + 3y = -12$
$x + y = -5$
$3x + 2y = 6$
$x - y = -2$
$4x - y = -4$

For questions 21 to 28, sketch each linear equation using any method.

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

For questions 29 to 40, reduce and sketch each linear equation using any method.

$y + 3 = -\dfrac{4}{5}x + 3$
$y - 4 = \dfrac{1}{2}x$
$x + 5y = -3 + 2y$
$3x - y = 4 + x - 2y$
$4x + 3y = 5 (x + y)$
$3x + 4y = 12 - 2y$
$2x - y = 2 - y \text{ (tricky)}$
$7x + 3y = 2(2x + 2y) + 6$
$x + y = -2x + 3$
$3x + 4y = 3y + 6$
$2(x + y) = -3(x + y) + 5$
$9x - y = 4x + 5$

<a class=”internal” href=”/intermediatealgebraberg/back-matter/answer-key-3-4/”>Answer Key 3.4

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