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.

\(x\)	\(y\)
\(-10\)
\(-5\)
\(0\)
\(5\)
\(10\)

Figure 7.7.1. \(2x-5y=10\)

Solution

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

\(x\)	\(y\)
\(-10\)	\(-6\)
\(-5\)	\(-4\)
\(0\)	\(-2\)
\(5\)	\(0\)
\(10\)	\(2\)

Figure 7.7.2. \(2x-5y=10\)

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.

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

Figure 7.7.3. \(-x-7y=3\)

Solution

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

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

Figure 7.7.4. \(-x-7y=3\)

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 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 \(-\frac{2}{3}\text{.}\)

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 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.