Chapter 2, Problem 1RE

Graphing a Linear Equation In Exercises 1-4, find the slope and $y\text{-intercept}$ (if possible) of the line. Sketch the line.

$y=-\frac{1}{2}x+1$

To determine

To calculate: The slope and $y-\text{intercept}$ of the line $y=-\frac{1}{2}x+1$ and also sketch the line.

Answer to Problem 1RE

The slope and $y-\text{intercept}$ of the line $y=-\frac{1}{2}x+1$ are $-\frac{1}{2}$ and $\left(0,1\right)$, respectively.

Explanation of Solution

Calculation:

Consider the equation,

$y=-\frac{1}{2}x+1$

The slope intercept form of the equation of line is given by the equation,

$y=mx+b$

Where, $m$ is the slope and $\left(0,b\right)$ is the $y-\text{intercept}$.

Write the equation in slope intercept form as,

$y=\left(-\frac{1}{2}\right)x+1$

On comparison of the equation with the slope intercept form, it is observed that the slope is,

$m=-\frac{1}{2}$

And, the $y-\text{intercept}$ is $\left(0,1\right)$.

Hence, the slope and $y-\text{intercept}$ of the line $y=-\frac{1}{2}x+1$ are $-\frac{1}{2}$ and $\left(0,1\right)$, respectively.

Graph:

The slope of $-\frac{1}{2}$ implies that the line falls half unit for each unit. The line moves to the right from the intercept $\left(0,1\right)$.

The sketch of the line $y=-\frac{1}{2}x+1$ is shown below as:

The graph of the equation $y=-\frac{1}{2}x+1$ is a straight line with negative slope of $-\frac{1}{2}$ and $y-\text{intercept}$ of $\left(0,1\right)$.