Textbook Question
Use a graphing calculator to solve each linear equation. 7x-2x+ 4-5=3x+1
2. Graphs of Equations
Lines
2:08 minutesProblem 23
Textbook Question
Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. vertical, through (-6, 4)
Verified step by step guidance1
Identify the type of line described: a vertical line. Vertical lines have an undefined slope and are represented by equations of the form \(x = a\), where \(a\) is the x-coordinate of every point on the line.
Since the line passes through the point \((-6, 4)\), the x-coordinate for all points on this vertical line is \(-6\).
Write the equation of the vertical line using the x-coordinate from the given point: \(x = -6\).
Confirm that this equation is in standard form. For vertical lines, the standard form is typically written as \(x = a\), which is already the case here.
No further simplification is needed, and the equation \(x = -6\) fully describes the vertical line through \((-6, 4)\).
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Equation of a Vertical Line
A vertical line has an undefined slope and is represented by an equation of the form x = a, where a is the x-coordinate of every point on the line. For example, a vertical line through (-6, 4) is x = -6, meaning all points have x = -6 regardless of y.
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Standard Form of Line Equations
Standard Form of a Linear Equation
The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A ≥ 0. Vertical lines can be written in this form by setting B = 0, such as x = -6 becoming 1x + 0y = -6.
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Slope-Intercept Form of a Linear Equation
The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Vertical lines cannot be expressed in this form because their slope is undefined, so only non-vertical lines can be written as y = mx + b.
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