Let's Learn Additional Practice Related to Lines

Section 7.7 Additional Practice Related to Lines

Exercises Exercises

Questions vary.

1.

Complete the entries in Figure 7.7.1 for the line with equation $2x-5y=10\text{.}$ Also, state the $x$ and $y$ intercepts of the line.

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$x$	$y$
$-10$
$-5$
$0$
$5$
$10$

Figure 7.7.1.

$2x-5y=10$

Solution

The $x$-intercept is $(5,0)$ and the $y$-intercept is $(0,-2)\text{.}$

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$x$	$y$
$-10$	$-6$
$-5$	$-4$
$0$	$-2$
$5$	$0$
$10$	$2$

Figure 7.7.2. $2x-5y=10$

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2.

Complete the entries in Figure 7.7.3 for the line with equation $-x-7y=3\text{.}$ Also, state the $x$ and $y$ intercepts of the line.

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$x$	$y$
$2$
	$-3$
$-2$
	$\frac{2}{7}$
	$-\frac{5}{14}$

Figure 7.7.3.

$-x-7y=3$

Solution

The $x$-intercept is $(-3,0)$ and the $y$-intercept is $\left(0,-\frac{3}{7}\right)\text{.}$

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$x$	$y$
$2$	$-\frac{5}{7}$
$-24$	$-3$
$-2$	$-\frac{1}{7}$
$-5$	$\frac{2}{7}$
$-\frac{1}{2}$	$-\frac{5}{14}$

Figure 7.7.4. $-x-7y=3$

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3.

Determine the slope of the line that passes through the points $(2,-2)$ and $(-4,16)\text{.}$

Solution

The slope is $-3\text{.}$

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4.

Determine the slope of the line that passes through the points $(6,2)$ and $(-6,-8)\text{.}$

Solution

The slope is $\frac{5}{6}\text{.}$

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5.

Determine the slope of the line shown in Figure 7.7.5.

A graph of the line that passes through the points $(-3,5)\text{,}$ $(0,3)\text{,}$ and $(3,1)\text{.}$ — Figure 7.7.5. Determine the slope of the line

Solution

The slope is $-\frac{2}{3}\text{.}$

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6.

A line with a slope of $\frac{4}{5}$ passes through the point $(-4,-7)\text{.}$ What is the $y$ -coordinate of the point on this line that has an $x$ -coordinate of $6\text{?}$

Solution

The $y$-coordinate is $1\text{.}$

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7.

A line with a slope of $-3$ passes through the point $(4,-14)\text{.}$ What is the $y$ -coordinate of the point that has an $x$ -coordinate of $-3\text{?}$

Solution

The $y$-coordinate is $7\text{.}$

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8.

A line with a slope of $-\frac{1}{2}$ passes through the point $(410,27)\text{.}$ What is the $x$ -coordinate of the point that a $y$ -coordinate of $24\text{?}$

Solution

The $x$-coordinate is $416\text{.}$

Use the slope-intercept form of the equation of a line to determine the equation of each described line.

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9.

Determine the equation of the line that has a slope of $\frac{11}{8}$ and a $y$ -intercept of $(0,-4)\text{.}$ Write the equation in slope-intercept form.

Solution

The equation is $y=\frac{11}{8}x-4$

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10.

Determine the equation of the line that has a slope of $-\frac{1}{3}$ and an $x$ -intercept of $(6,0)\text{.}$ Write the equation in slope-intercept form.

Solution

The equation is $y=-\frac{1}{3}x+2\text{.}$

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11.

Determine the equation of the line that passes through the points $(1,12)$ and $(-3,-8)\text{.}$ Write the equation in slope-intercept form.

Solution

The equation is $y=5x+7\text{.}$

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12.

Determine the equation of the line shown in Figure 7.7.6. Write the equation in slope-intercept form.

A graph of the line that passes through the points $(-1,-3)\text{,}$ $(0,-1)\text{,}$ and $(1,1)\text{.}$ — Figure 7.7.6. Determine the slope of the line

Solution

The equation is $y=\frac{5}{2}x-1\text{.}$

Use the point-slope form of the equation of a line to determine the equation of the line that passes through each pair of points. State your final answer in slope-intercept form.

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