Exercise 4 Page 171

Let's assume that the slope

m

and the point

(x_{0}, y_{0})

are given. In order to write an equation for a line that passes through

(x_{0}, y_{0})

with a slope

m,

we will use the Slope Formula.

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

In the formula,

(x_{1}, y_{1})

and

(x_{2}, y_{2})

are the points that appear on the line and

m

is the slope of the line. Therefore, we will assume that

(x, y)

is any point that our line passes through different than

(x_{0}, y_{0}) .

Let's apply the formula.

m = \frac{y - y _{0}}{x - x _{0}}

Next, we will multiply both sides of the equation by

(x - x_{0})

to simplify it.

(x - x_{0}) \cdot m (x - x_{0}) \cdot m = (x - x_{0}) \cdot \frac{y - y _{0}}{x - x _{0}} = y - y_{0}

Finally, we will rearrange the equation such that the

y -

variable will be on the left-hand side and the

x -

variables will be on the right-hand side.

y - y_{0} = m (x - x_{0})

As a result, we have written our equation in point-slope form.