Chapter 1.4, Problem 109AYU

In Problems 109-112, write an equation of each line. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer.

To determine

To find: The equation of the line, given in figure, either in general form or slope intercept form.

Answer to Problem 109AYU

Solution:

$y=-x+1$   Or  $y+x=1$

Explanation of Solution

Given:

The following figure

Formula used:

Slope of a line $m= \frac{y_2-y_1}{x_2-x_1}$

The equation of a line in general form: $Ax+By=C$

The equation of a line in Slope intercept form: $y-y_1=m(x-x_1)$

Calculation:

The two points identified on the line are $(3,\text{ 0)}$ and $(0,\text{ 1)}$. Using these points find the slope of the line, $(x_1,y_1)=\left(3,0\right);(x_2,y_2)=\left(0,1\right)$

$m= \frac{y_2-y_1}{x_2-x_1}$

$=\frac{1-0}{0-3}$

$=\frac{1}{-3}$

$=-\frac{1}{3}$

The slope of the line $m=-\frac{1}{3}$. Use the slope $m=-\frac{1}{3}$ and the point $\left(3,0\right)$ to find the slope intercept form of the equation of the line

$y-y_1=m(x-x_1)$

$y-0=-\frac{1}{3} \left(x-3\right)$

$3y=-x+1$   Multiply both sides with 3

$3y+x=-x+1+x$

$x+3y=1$

Or   $x+3y=1$