Chapter 1, Problem 2CT

To determine

To find : the equation of the line.

Answer to Problem 2CT

the equation of line is $y=-x+1$.

Explanation of Solution

Given information :

Points are $\left(2,-1\right),\left(-3,4\right)$.

Formula used :

Slope of the line passing through the points is $\frac{y_2-y_1}{x_2-x_1}$

The equation of line is $y=mx+c$.

Calculation: since the points are $\left(2,-1\right),\left(-3,4\right)$ ,

So the Slope of the line passing through the points is $\frac{y_2-y_1}{x_2-x_1}$

  $\begin{array}{l}\frac{y_2-y_1}{x_2-x_1}=\frac{4-\left(-1\right)}{-3-\left(2\right)}\text{ [substitute]}\\ \frac{y_2-y_1}{x_2-x_1}=\frac{5}{-5}\text{ [simplify]}\\ \frac{y_2-y_1}{x_2-x_1}=-1\text{ [divide]}\end{array}$

Now, substitute the value of slope in the equation,

Since slope of the line is $-1$ so the equation,

  $\begin{array}{l}y=mx+c\\ y=-1x+c\text{ [substitute]}\\ y=-x+c\text{ [simplify]}\end{array}$

Now find the value of $c$ , substitute $x=2,y=-1$

  $\begin{array}{l}y=-x+c\\ -1=-2+c\text{ [substitute }x=2,y=-1]\\ c=1\text{ [simplify}]\end{array}$

Thus, the equation of the line is $y=-x+1$.