Chapter 1.3, Problem 108AYU

In Problems $115-118$, write an equation of each line. Express your answer using either the general form of the equation of a line, whichever you prefer.

To determine

The equation of line for the graph below in either the slope-intercept form of equation of line or the general form of equation of line,

Answer to Problem 108AYU

Solution:

The equation of the line for the given graph is;

The slope-intercept form of equation of line is $y=-x+1$.

The general form of equation of line is $x+y=1$.

Explanation of Solution

Given Information:

The graph is,

Explanation:

Consider the graph,

If $P=\left(x_1,y_1\right)$ and $Q=\left(x_2,y_2\right)$ are two distinct points and $x_1\ne x_2$, the slope $m$ of the nonvertical line $L$ containing $P$ and $Q$ is defined by the formula $m=\frac{y_2-y_1}{x_2-x_1}$.

From graph, the points through which the line is passing are $\left(0,1\right)$ and $\left(1,0\right)$.

Therefore, plug $x_1=0$, $y_1=1$, $x_2=1$, $y_2=0$ in the formula of slope.

$\Rightarrow m=\frac{0-1}{1-0}$

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

Thus, slope is, $m=-1$.

The point slope form of an equation of a non-vertical line with slope $m$ that contains the point $\left(x_1,y_1\right)$ is, $y-y_1=m\left(x-x_1\right)$.

Thus, plug $m=-1$, $y_1=1$, $x_1=0$ in the point slope form to find the $y$-intercept.

$y-1=-1\left(x-0\right)$

$\Rightarrow y-1=-x$

$\Rightarrow y-1+1=-x+1$

$\Rightarrow y=-x+1$

The slope-intercept form of an equation line is $y=mx+b$ where the slope is $m$ and the $y-\text{intercept}$ is $b$.

Therefore, the slope-intercept form of an equation of line is $y=-x+1$.

The equation of line in general form is $Ax+By=C$ where $A,B$, and $C$ are real numbers and $A$, and $B$ are not both 0.

Consider equation $y=-x+1$,

$\Rightarrow x+y=1$

Therefore, the general form of equation of line is $x+y=1$.