/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 250 Find the slope of each line. \... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 250

Find the slope of each line. \(x=-4\)

Short Answer

Expert verified
The slope is undefined.

Step by step solution

01

Identify the equation form

Recognize that the equation given is of the form \(x = a\), where \(a\) is a constant.
02

Understand the type of line

Recall that an equation of the form \(x = a\) represents a vertical line in the coordinate plane.
03

Determine the slope

Vertical lines have an undefined slope because the change in the x-coordinate is 0, which would result in a division by zero in the slope formula.
04

Conclude the slope

Thus, the slope of the line given by \(x = -4\) is undefined.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Vertical Lines
A vertical line on the coordinate plane is special because it runs straight up and down. When you look at the equation of a vertical line, it is always in the form of \(x = a\), where \(a\) is a constant number. This means that no matter what \(y\) value you choose, \(x\) will always be \(a\). For example, \(x = -4\) means that all points on this line have \(x\) as -4.
Knowing that vertical lines have this unique trait can help you easily recognize them in equations and graphs.
Undefined Slope
The slope of a line tells us how steep the line is. Normally, we calculate the slope using the formula \( \text{slope} = \frac{{\Delta y}}{{\Delta x}} \), where \( \Delta y\) is the change in \(y\) and \( \Delta x\) is the change in \(x\).
However, with vertical lines like \(x = -4\), \( \Delta x\) is always 0 because there's no change in the \(x\) value. When you try to divide by 0, the result is undefined. That's why we say vertical lines have an undefined slope鈥攊t's a way to avoid dividing by zero.
Coordinate Plane
The coordinate plane is a two-dimensional surface where we can plot points, lines, and curves. It has a horizontal axis called the \(x\)-axis and a vertical axis called the \(y\)-axis. The point where these two axes intersect is called the origin, marked as \( (0,0) \).
Understanding how to navigate the coordinate plane is key to solving many math problems. It lets you visualize equations and makes concepts like the slope easier to grasp.
Each point on the plane is defined by a pair of numbers, \( (x,y) \), that tell you how far to move horizontally and vertically from the origin.

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Most popular questions from this chapter

Find the equation of a line containing the given points. Write the equation in slope-intercept form. (3,5) and (-7,5)

Graph the linear inequality \(y \leq-x\)

Determine whether each ordered pair is a solution to the inequality \(y>x-3\) : (a) (0,0) (b) (2,1) (c) (-1,-5) (d) (-6,-3) (e) (1,0)

Graph the linear inequality \(x+5 y<-5\)

Find an equation of a line parallel to the given line and contains the given point. Write the equation in slope-intercept form. line \(y=4 x+2,\) point (1,2)
See all solutions

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