Chapter 1, Problem 18RE

In Problems 18-25, find an equation of the line having the given characteristics. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Graph the line.

$\text{Slope }=-2$; containing the point $\left(3,-1\right)$

To determine

To find: The equation of a line having slope $-2$ and containing the point $\left(3,-1\right)$. To also sketch a graph of the equation.

Answer to Problem 18RE

Solution:

The general form of equation of the line is $2x+y=5$.

Explanation of Solution

Given:

The slope of the line is $-2$ and containing the point $\left(3,-1\right)$

Formula used:

Point slope form of an equation of a line.

$(y-y₁)=m(x-x₁)$

Calculation:

$\left(y-\left(-1\right)\right)=\left(-2\right)\left(x-3\right)$

$\left(y+1\right)=-2x+6$

$y+1+2x=-2x+6+2x$   Add $2x$ to both sides.

$2x+y+1=6$

$2x+y+1-1=6-1$   Subtract 1 from both sides.

$2x+y=5$

The general form of equation of the line is $2x+y=5$.