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Chapter 2: Problem 53

What is the slope of a line defined by \(y=-7 ?\)

Short Answer

Expert verified
The slope is 0.

Step by step solution

01

Identify the Form of the Line Equation

The given equation of the line is in the form: y = mx + b. Here, y = -7. The equation does not have an x term.
02

Recognize the Slope-Intercept Form

In the slope-intercept form of the line equation, y = mx + b, the coefficient m represents the slope. In this equation, y = -7, the x term is missing, which implies that the slope m is 0 because any x term would be multiplied by 0.
03

Conclude the Slope

When the equation is y = -7, it describes a horizontal line. The slope (m) of a horizontal line is always 0.

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Key Concepts

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

horizontal line
A horizontal line is a line that runs from left to right and has the same y-coordinate for all its points. Imagine a perfectly flat surface, like the horizon when you look out at the ocean.
In the equation form, a horizontal line can be represented as: y = c where c is a constant. This means regardless of the x-value, y remains the same.
It's clear that there's no change in y as x changes, which leads to a slope of 0.
slope-intercept form
The slope-intercept form is a common way to write the equation of a line. It is given by: y = mx + b Here, y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.
This form helps to identify the slope and y-intercept easily, making it ideal for graphing linear equations. The exercise given, y = -7, is also in this form, but with no x term, implying a slope (m) of 0.
coefficient
In the context of the equation of a line, a coefficient is a numerical value assigned to a variable. Particularly in the slope-intercept form, y = mx + b, m is the coefficient of x. This coefficient, m, represents the slope of the line.
When we look at y = -7, we see there's no x term, meaning the coefficient of x is 0. Hence, the slope of the line is 0, confirming it is a horizontal line.
Understanding coefficients helps in quickly determining the behavior and orientation of a line on a graph.

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Most popular questions from this chapter

Refer to the functions \(r, p,\) and \(q .\) Evaluate the function and write the domain in interval notation. \(r(x)=-3 x \quad p(x)=x^{2}+3 x \quad q(x)=\sqrt{1-x}\) $$\left(\frac{p}{q}\right)(x)$$

a. Graph \(a(x)=x\) for \(x<1\). b. Graph \(b(x)=\sqrt{x-1}\) for \(x \geq 1\). c. Graph \(c(x)=\left\\{\begin{array}{ll}x & \text { for } x<1 \\ \sqrt{x-1} & \text { for } x \geq 1\end{array}\right.\)

a. Graph \(m(x)=\frac{1}{2} x-2\) for \(x \leq-2\). b. Graph \(n(x)=-x+1\) for \(x>-2\). c. Graph \(t(x)=\left\\{\begin{array}{ll}\frac{1}{2} x-2 & \text { for } x \leq-2 \\ -x+1 & \text { for } x>-2\end{array}\right.\)

Graph the function.$$ n(x)=\left\\{\begin{aligned} -4 & \text { for }-3

Given \(f(x)=4 \sqrt{x}\) a. Find the difference quotient (do not simplify). b. Evaluate the difference quotient for \(x=1\), and the following values of \(h: h=1, h=0.1, h=0.01,\) and \(h=0.001\). Round to 4 decimal places. c. What value does the difference quotient seem to be approaching as \(h\) gets close to \(0 ?\)
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