Exercise 39 Page 178

The Slope Formula is used to determine the slope

m

of the line that connects two given points,

(x_{1}, y_{1})

and

(x_{2}, y_{2}) .

m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

In this case, however, we have been given the slope of a line and two points with a missing coordinate. When we substitute these values into the Slope Formula, it does not matter which point we choose to use as

(x_{1}, y_{1})

or

(x_{2}, y_{2}) .

Both will give the same result.

- \frac{1}{2} = \frac{4 - 8}{r - ( - 2 )} or - \frac{1}{2} = \frac{8 - 4}{- 2 - r}

Here we will use the points in the given order and solve for the unknown coordinate.

m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

SubstitutePoints

Substitute $(- 2, 8)$ & $(r, 4)$

m = \frac{4 - 8}{r - ( - 2 )}

Substitute

$m = - \frac{1}{2}$

- \frac{1}{2} = \frac{4 - 8}{r - ( - 2 )}

▼

Solve for

r

SubNeg

$a - (- b) = a + b$

- \frac{1}{2} = \frac{4 - 8}{r + 2}

SubTerm

Subtract term

- \frac{1}{2} = \frac{- 4}{r + 2}

MultEqn

$LHS \cdot (r + 2) = RHS \cdot (r + 2)$

(r + 2) (- \frac{1}{2}) = - 4

MultEqn

$LHS \cdot (- 2) = RHS \cdot (- 2)$

- 2 (r + 2) (- \frac{1}{2}) = 8

CommutativePropMult

Commutative Property of Multiplication

- 2 (- \frac{1}{2}) (r + 2) = 8

MultNegNegOnePar

$- a (- b) = a \cdot b$

2 (\frac{1}{2}) (r + 2) = 8

MoveLeftFacToNum

$a \cdot \frac{b}{c} = \frac{a \cdot b}{c}$

\frac{2}{2} (r + 2) = 8

CalcQuot

Calculate quotient

1 (r + 2) = 8

IdPropMult

Identity Property of Multiplication

r + 2 = 8

SubEqn

$LHS - 2 = RHS - 2$

r = 6

When

r = 6,

the line passes through both points.