How do you write an equation in the point-slope form of the line that passes through the given points (-1, -8), (4, -6)?

Solution:

Given, the points are (-1, -8) and (4, -6)

We have to write an equation of the line in the point slope form.

The equation of the line in point-slope form is given by

\((y-y_{1})=m(x-x_{1})\)

Using the formula find the slope m,

\(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Here, (x₁, y₁) = (-1, -8) and (x₂, y₂) = (4, -6). Then the slope is

\(m=\frac{-6-(-8)}{4-(-1)}\\=\frac{-6+8}{4+1}\\=\frac{2}{5}\)

Now, put the value of m in point-slope form equation and use the point (-1, -8),

\((y-(-8))=\frac{2}{5}(x-(-1))\\(y+8)=\frac{2}{5}(x+1)\)

Therefore, the equation of the line is \((y+8)=\frac{2}{5}(x+1)\).

How do you write an equation in the point-slope form of the line that passes through the given points (-1, -8), (4, -6)?

Summary:

An equation in the point-slope form of the line that passes through the given points (-1, -8), (4, -6) is \((y+8)=\frac{2}{5}(x+1)\).