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}{3} = \frac{3 - r}{6 - 9} or - \frac{1}{3} = \frac{r - 3}{9 - 6}

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 $(9, r)$ & $(6, 3)$

m = \frac{3 - r}{6 - 9}

SubstituteIII

Substitute $m = - \frac{1}{3}$

- \frac{1}{3} = \frac{3 - r}{6 - 9}

▼

Solve for

r

SubTerm

Subtract term

- \frac{1}{3} = \frac{r - 3}{3}

MultEqn

$LHS \cdot 3 = RHS \cdot 3$

- 1 = r - 3

AddEqn

$LHS + 3 = RHS + 3$

2 = r

RearrangeEqn

Rearrange equation

r = 2

When

r = 2,

the line passes through both points.

Exercise 76 Page 232

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