Exercise 1 Page 241

We are given the slope and a point that lies on the line. This is enough information to write the equation in point-slope form. Let's do this first and then we will rewrite it in standard form. We can write the equation in point-slope form by substituting $\text{-}2$ for $m$ and $(1,7)$ for $(x_1,y_1).$

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

Substitute

$m=\text{-}2$

$y-y_1=\text{-}2(x-x_1)$

SubstituteII

$x_1=1$, $y_1=7$

$y-7=\text{-}2(x-1)$

Now that we have the equation in point-slope form, let's rearrange it until it is in standard form.

$$\begin{array}{c}Ax+By=C\end{array}$$

In the above formula, $A,$ $B,$ and $C$ are constants. We will start by distributing $\text{-}2.$

$y-7=\text{-}2(x-1)$

Distr

Distribute $\text{-}2$

$y-7=\text{-}2x+2$

AddEqn

$\text{LHS}+7=\text{RHS}+7$

$y=\text{-}2x+9$

AddEqn

$\text{LHS}+2x=\text{RHS}+2x$

$y+2x=9$

CommutativePropAdd

Commutative Property of Addition

$2x+y=9$

We have rewritten the equation of the line in standard form.

$$\begin{array}{c}2x+y=9\end{array}$$

In this case, $A=2,$ $B=1,$ and $C=9.$