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. y-y_1=m(x-x_1) 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 - 2 for m and (1,7) for (x_1,y_1).

y-y_1=m(x-x_1)

Substitute

m= - 2

y-y_1= - 2(x-x_1)

SubstituteII

x_1= 1, y_1= 7

y- 7=- 2(x- 1)

Now that we have the equation in point-slope form, let's rearrange it until it is in standard form. Ax+By=C In the above formula, A, B, and C are constants. We will start by distributing - 2.

y-7=- 2(x-1)

Distr

Distribute - 2

y-7=- 2x+2

AddEqn

LHS+7=RHS+7

y=- 2x+9

AddEqn

LHS+2x=RHS+2x

y+2x=9

CommutativePropAdd

Commutative Property of Addition

2x+y=9

We have rewritten the equation of the line in standard form. 2x+y=9 In this case, A=2, B=1, and C=9.