Exercise 63 Page 273

m = y_2-y_1/x_2-x_1 Note that it does not matter which point we choose to use for ( x_1, y_1) and ( x_2, y_2), since the result of using the Slope Formula will be the same.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 6,- 8) & ( 3,- 4)

m=- 4-( - 8)/3- 6

▼

Add and subtract terms

SubNeg

a-(- b)=a+b

m=- 4 + 8/3-6

AddSubTerms

Add and subtract terms

m=4/- 3

MoveNegDenomToFrac

Put minus sign in front of fraction

m=- 4/3

Now, knowing the slope we can find the equation of the line. Equations in slope-intercept form follow a certain format. y=mx+ b In this format m is the slope and b is the y-intercept. The line has a slope of - 43, which means that we can substitute m=- 43. y=- 4/3x+ b To write a complete equation for this line, we also need to determine the y-intercept b. We can do that by substituting one of the given points into the equation and solving for b. Let's use (6,- 8).

y=- 4/3x+b

SubstituteII

x= 6, y= - 8

- 8=- 4/3( 6)+b

▼

Solve for b

MoveRightFacToNum

a/c* b = a* b/c

- 8=- 24/3+b

CalcQuot

Calculate quotient

- 8=- 8 +b

AddEqn

LHS+8=RHS+8

0=b

RearrangeEqn

Rearrange equation

b= 0

Now that we have both the slope and the y-intercept, we can write the final equation. y=- 4/3x+ 0 ⇔ y=- 4/3x