Chapter 0.1, Problem 26E

(a)

To determine

To find the slope of the line $x+y=2$ .

Answer to Problem 26E

The slope of the line $x+y=2$ is $-1$ .

Explanation of Solution

Given the equation of a line:

  $x+y=2$

Concept Used:

Slope-Intercept form of a line:

Suppose that the equation of a line is given in the slope-intercept form: $y=mx+c$ .

Then, the $m$ gives the slope of the line and $c$ gives the $y$ -intercept of the line.

Calculation:

Given the equation of the line:

  $x+y=2$ .

Write $x+y=2$ in the slope intercept form:

  $\begin{array}{c}x+y=2\\ y=2-x\\ y=-x+2\end{array}$ .

Thus, the slope-intercept form of the line:

  $y=-x+2$ .

Compare $y=-x+2$ with the general slope-intercept form and observe that the slope of the line is $-1$ .

Conclusion:

The slope of the line $x+y=2$ is $-1$ .

(b)

To determine

To find the $y$ -intercept of the line $x+y=2$ .

Answer to Problem 26E

The $y$ -intercept of the line $x+y=2$ is $2$ .

Explanation of Solution

Given the equation of a line:

  $x+y=2$

Concept Used:

Slope-Intercept form of a line:

Suppose that the equation of a line is given in the slope-intercept form: $y=mx+c$ .

Then, the $m$ gives the slope of the line and $c$ gives the $y$ -intercept of the line.

Calculation:

Given the equation of the line:

  $x+y=2$ .

Write $x+y=2$ in the slope-intercept form:

  $\begin{array}{c}x+y=2\\ y=2-x\\ y=-x+2\end{array}$ .

Thus, the slope-intercept form of the line:

  $y=-x+2$ .

Compare $y=-x+2$ with the general slope-intercept form and observe that the $y$ -intercept of the line is $2$ .

Conclusion:

The $y$ -intercept of the line $x+y=2$ is $2$ .

(c)

To determine

To graph the line $x+y=2$ .

Explanation of Solution

Given the line:

  $x+y=2$ .

Graph the line with the help of a graphing calculator: