Problem 96
Question
Explain how to graph the equation \(x=2 .\) Can this equation be expressed in slope-intercept form? Explain.
Step-by-Step Solution
Verified Answer
The equation \(x=2\) is graphed as a vertical line passing at the point \(x=2\). It cannot be expressed in slope-intercept form since a vertical line does not have a defined slope and a y-intercept.
1Step 1: Graphing the Equation
To graph the equation \(x=2\), plot a vertical line at \(x=2\) on the Cartesian graph, such line passes through all points with \(x\) coordinate equals 2. This represents all solutions to the equation, which are points of the form \((2,y)\), where y is any real number.
2Step 2: Evaluating Slope-Intercept Form
The slope-intercept form of a linear equation is expressed as \(y=mx+b\), where \(m\) is the slope of the line and \(b\) is the y-intercept. The given equation \(x=2\) has no \(y\) term, so it can't be expressed in slope-intercept form due to lacking a 'slope' and 'y-intercept'. A vertical line has an undefined slope and does not intercept the y-axis at any point.
Other exercises in this chapter
Problem 96
Let \(f\) and \(g\) be defined by the following table: $$\begin{array}{ccc} x & f(x) & g(x) \\ \hline-2 & 6 & 0 \\ -1 & 3 & 4 \\ 0 & -1 & 1 \\ 1 & -4 & -3 \\ 2
View solution Problem 96
Begin by graphing the standard cubic function, \(f(x)=x^{3} .\) Then use transformations of this graph to graph the given function. $$g(x)=x^{3}-2$$
View solution Problem 97
A tangent line to a circle is a line that intersects the circle at exactly one point. The tangent line is perpendicular to the radius of the circle at this poin
View solution Problem 97
Find \(f(-x)-f(x)\) for the given function \(f\) Then simplify the expression. $$f(x)=x^{3}+x-5$$
View solution