Exercise 4 Page 215

We want to write an equation of a line in standard form. We are given a slope and a point that lies on the line. With this information we can write the equation in point-slope form. Then, we will rewrite it in standard form. Let's recall the general formula for an equation in point-slope form! y- y_1= m(x- x_1) In this equation, m represents slope, ( x_1, y_1) represents a specific point on the line, and (x,y) represents any point also on the line. Graphically, this means that the line passes through the point ( x_1, y_1). Therefore, we can write the equation in point-slope form by substituting - 2 for m and ( - 7, - 10) for ( x_1, y_1) into the formula.

y-y_1=m(x-x_1)

Substitute

m= - 2

y-y_1= - 2(x-x_1)

SubstituteII

x_1= - 7, y_1= - 10

y-( - 10)=- 2(x-( - 7))

SubNeg

a-(- b)=a+b

y+10=- 2(x+7)

We found the equation of the line in point-slope form. Next, we will rewrite it to obtain it in standard form. Ax+ By= C In the formula, A, B, and C are constants and A and B cannot both be equal 0. To rewrite our equation in this form, we will start by distributing - 2.

y+10=- 2(x+7)

Distr

Distribute - 2

y+10=- 2x-14

SubEqn

LHS-10=RHS-10

y=- 2x-24

AddEqn

LHS+2x=RHS+2x

y+2x=- 24

CommutativePropAdd

Commutative Property of Addition

2x+y=- 24

Let's check if this is an equation written in standard form. Ax+ By &= C 2x+ 1y &= - 24 In our case, A= 2, B= 1, and C= - 24. This means that the equation is written in standard form.