2.1.1: Exercises 2.1
- Page ID
- 62898
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Terms and Concepts
Exercise \(\PageIndex{1}\)
Explain the difference between point-slope form and slope-intercept form.
- Answer
-
Answers will vary.
Exercise \(\PageIndex{2}\)
To uniquely determine a line, what information do you need?
- Answer
-
A point and a slope, or two points
Exercise \(\PageIndex{3}\)
What is the slope of a horizontal line?
- Answer
-
\(m=0\)
Exercise \(\PageIndex{4}\)
A line goes through the point \((0,6)\). Is this the y-intercept of the line or the x-intercept of the line? Explain.
- Answer
-
This is the y-intercept because \(x=0\) so it is where the line crosses the y-axis.
Exercise \(\PageIndex{5}\)
Line 1 has a slope of \(m_1=2\). If line 2 is parallel to line 1, what is \(m_2\)?
- Answer
-
\(m_2=2\)
Exercise \(\PageIndex{6}\)
Line 1 has a slope of \(m_1=-4\). If line 2 is perpendicular to line 1, what is \(m_2\)?
- Answer
-
\(m_2=\frac{1}{4}\)
Problems
In exercises \(\PageIndex{7}\) - \(\PageIndex{16}\), write an equation for each line in the indicated form.
Exercise \(\PageIndex{7}\)
Write the equation in point-slope form for the line that passes through \((1,2)\) and is parallel to the line \(2x+y=5\).
- Answer
-
\(y-2=-2(x-1)\)
Exercise \(\PageIndex{8}\)
Write the equation of the line in slope-intercept form passing through the points \((1,2)\) and \((-1,4)\).
- Answer
-
\(y=-x+3\)
Exercise \(\PageIndex{9}\)
Write the equation in point-slope form for the line that passes through \((0,4)\) and is perpendicular to the line \(x-2y=6\).
- Answer
-
\(y-4=-2(x-0)\)
Exercise \(\PageIndex{10}\)
Write the equation of the line in slope-intercept form passing through the points \((-1,0)\) and \((3,6)\).
- Answer
-
\(y=\frac{3}{2}x + \frac{3}{2}\)
Exercise \(\PageIndex{11}\)
Write the equation of the line in slope-intercept form passing through the points \((-2,1)\) and \((2,7)\).
- Answer
-
\(y=\frac{3}{2}x + 4\)
Exercise \(\PageIndex{12}\)
Consider the linear function \(f(x)=2x-8\). What is the value of the function when \(x=0.1\)?
- Answer
-
\(-7.8\)
Exercise \(\PageIndex{13}\)
Write the equation in slope-intercept form for the line that passes through \((-2,2)\) and is perpendicular to the line \(x+3y=8\).
- Answer
-
\(y=3x+8\)
Exercise \(\PageIndex{14}\)
Write the equation in point-slope form of the line that passing through the points \((3,6)\) and \((7,4)\).
- Answer
-
\(y-4=\frac{1}{2}(x-7)\), or \(y-6=-\frac{1}{2}(x-3)\)
Exercise \(\PageIndex{15}\)
Write the equation of the line passing through the points \((-4,4)\) and \((0,-4)\) in slope-intercept form.
- Answer
-
\(y=-2x-4\)
Exercise \(\PageIndex{16}\)
Write the equation of the line parallel to \(y=6x+4\) that has a y-intercept of \(2\) in point-slope form.
- Answer
-
\(y-2=6(x-0)\)
In exercises \(\PageIndex{17}\) - \(\PageIndex{20}\), answer each question about the properties of the given line(s).
Exercise \(\PageIndex{17}\)
Consider the linear function \(g(x)=-4x+5\). What is the slope of the function when \(x=4\)?
- Answer
-
\(m=-4\)
Exercise \(\PageIndex{18}\)
Determine the x-intercept of the line \(y=4x-8\).
- Answer
-
\((2,0)\)
Exercise \(\PageIndex{19}\)
Determine the y-intercept of the line \(y=4x-8\).
- Answer
-
\((0,-8)\)
Exercise \(\PageIndex{20}\)
Which line has a steeper slope: \(y=5x+10\) or the line passing through the points \((-5,0)\) and \((0,11)\)?
- Answer
-
The line \(y=5x+10\) has a steeper slope.