Chapter B, Problem 14E

To determine

To find: The equation of the line for the given conditions.

Answer to Problem 14E

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

Explanation of Solution

Given:

The required line is passing through the points $\left(-1,-2\right)$ and $\left(4,3\right)$.

Property used:

The equation of the line passes through the point $\left(x_1,y_1\right)$ and having slope m is, $y-y_1=m\left(x-x_1\right)$.

Calculation:

To find the slope, solve the equation,

$\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ 3-\left(-2\right)=m\left(4-\left(-1\right)\right)\\ \frac{3+2}{4+1}=m\\ \frac{5}{5}=m\\ 1=m\end{array}$

Therefore, $m=1$.

Consider the given point be $\left(x_1,y_1\right)=\left(-1,-2\right)$ and the slope m = $-5$.

Substitute the values in the property mentioned above.

$\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ y-\left(-2\right)=1\left(x-\left(-1\right)\right)\\ y+2=x+1\\ y=x+1-2\\ y=x-1\end{array}$

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