Hello!
Recall that point-slope form is written as [tex]y-y_{1}=m(x- x_{1})[/tex]. In this form, m is the slope and [tex]x_{1}[/tex] and [tex]x_{1}[/tex] is a given point. Therefore, there are two options to write this equation. Although, their slopes must be equal if there are two different equations.
Now, let's find the slope. To find the slope, use the formula: [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex].
Now, we can substitute the given points to find the slope.
[tex]\frac{2- (-3)}{2-(-8)} = \frac{5}{10} = \frac{1}{2}[/tex] | The slope of the two points is m = 2.
Now, we can write the equations.
Using the point (-8, -3): y + 3 = 2(x + 8)
Using the point (2, 2): y - 2 = 2(x - 2)
Those two equations are your final answers.
