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Chapter 0: Problem 12

Graph. List the slope and \(y\) -intercept. $$f(x)=-0.5 x$$

Short Answer

Expert verified
Slope is \( -0.5 \) and y-intercept is \( 0 \).

Step by step solution

01

- Understand the Slope-Intercept Form

The slope-intercept form of a linear equation is written as: \[ y = mx + b \] Here, \( m \) represents the slope and \( b \) represents the y-intercept.
02

- Identify the Slope

In the given function, \( f(x) = -0.5x \), compare it with the slope-intercept form. \( m = -0.5 \). Therefore, the slope \( m \) is \( -0.5 \).
03

- Identify the Y-Intercept

In the given function, there is no constant term added to \( -0.5x \). Thus, \( b = 0 \). Therefore, the y-intercept \( b \) is \( 0 \).

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Key Concepts

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

slope-intercept form
The slope-intercept form is super handy when graphing linear equations. It looks like this: \[ y = mx + b \] where, \[ m \] stands for the slope of the line, and \[ b \] signifies the y-intercept. The reason it鈥檚 called slope-intercept form is that it gives you direct information about the slope and the y-intercept. Once you have this form, it's straightforward to plot the line on a graph. Just start at the y-intercept point on the y-axis, and use the slope to find the next points. It makes graphing linear equations a piece of cake!
slope
The slope is a crucial part of a linear equation. It's represented by the letter \[ m \]. The slope tells you how steep the line is. Imagine a hill - the steeper the hill, the higher the slope. In mathematical terms, the slope shows the rate of change of the y-variable with respect to the x-variable. So if your equation is \[ y = -0.5x \], the slope is \[ -0.5 \]. That negative sign means the line is going downwards as it moves to the right. A positive slope means the line goes upwards. To graph a line using its slope, you start at a point and move up or down (depending on the slope's sign) and then to the right.
y-intercept
The y-intercept is the point where the line crosses the y-axis. It's depicted by the letter \[ b \] in the slope-intercept form. In simpler words, it's where your line hits the y-axis when x is zero. For the equation \[ f(x) = -0.5x \], there's no constant term added or subtracted. That means the y-intercept \[ b \] is 0. So, the line crosses the y-axis at (0, 0). When graphing, the y-intercept is your starting point. From there, use the slope to find other points on the line.

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