Assume that (x,y) is any point that the line passes through different than the given point. Then, consider the Slope Formula to write an equation for the line.
See solution.
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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 = 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=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)* m&=( x- x_0)* y- y_0/x- x_0
( x- x_0)* m&= 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.
