Exercise 33 Page 154

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}}

Here, we are given the slope of a line and two points, one of them 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.

- 1 = \frac{0 - k}{2 - ( - 2 )} or - 1 = \frac{k - 0}{- 2 - 2}

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}}

SubstituteValues

Substitute values

- 1 = \frac{k - 0}{- 2 - 2}

▼

Solve for

k

SubTerms

Subtract terms

- 1 = \frac{k}{- 4}

MultEqn

$LHS \cdot (- 4) = RHS \cdot (- 4)$

- 4 (- 1) = k

MultNegNegOnePar

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

4 = k

RearrangeEqn

Rearrange equation

k = 4