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## Section6.7Additional Practice Related to Lines

### Subsection6.7.1Exercises

Questions vary.

###### 1

Complete the entries in Table 6.7.1 for the line with equation $2x-5y=10\text{.}$ Also, state the $x$ and $y$ intercepts of the line.

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

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

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

Complete the entries in Table 6.7.3 for the line with equation $-x-7y=3\text{.}$ Also, state the $x$ and $y$ intercepts of the line.

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

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

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

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

Solution

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

###### 4

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

Solution

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

###### 5

Determine the slope of the line shown in Figure 6.7.5.

Solution

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

###### 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 $1\text{.}$

###### 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 $7\text{.}$

###### 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.

###### 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 $y=\frac{11}{8}x-4$

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

###### 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 $y=5x+7\text{.}$

###### 12

Determine the equation of the line shown in Figure 6.7.6. Write the equation in slope-intercept form.

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.

###### 13

$(9,-2)$ and $(7,-8)$

Solution

The equation of the line is $y=3x-29\text{.}$

###### 14

$(-3,5)$ and $(5,1)$

Solution

The equation of the line is $y=-\frac{1}{2}x+\frac{7}{2}\text{.}$

###### 15

$(-11,0)$ and $(-9,2)$

Solution

The equation of the line is $y=x+11\text{.}$

###### 16

$(0,7)$ and $(-3,10)$

Solution

The equation of the line is $y=-x+7\text{.}$

Questions vary.

###### 17

What are the equations of the vertical and horizontal lines that pass through the point $(9,2)\text{?}$

Solution

The vertical line's equation is $x=9$ and the horizontal line's equation is $y=2\text{.}$

###### 18

What is the slope of any line that is parallel to the line with equation $6x-10y=7\text{?}$

Solution

The slope is $\frac{3}{5}\text{.}$

###### 19

What is the slope of any line that is perpendicular to the line with equation $y=-\frac{1}{8}x+11\text{?}$

Solution

The slope is $8\text{.}$