Answer:
The equation in point-slope form is: [tex]y+4=\frac{-1}{10}(x+1)[/tex]
Step-by-step explanation:
Write the equation of the line that passes through the points (-1,-4) and (9,-5).
The point slope form is: [tex]y-y_1=m(x-x_1)[/tex]
Where m is slope and x₁ and y₁ are the points given
Finding Slope
Slope can be found of given points using formula: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
We have [tex]x_1=-1, y_1=-4, x_2=9, y_2=-5[/tex]
Putting values and finding slope
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-5-(-4)}{9-(-1)}\\ Slope=\frac{-5+4}{9+1}\\ Slope=\frac{-1}{10}[/tex]
So, slope m = -1/10
Using point (-1,-4) and slope m = -1/10 the equation is:
[tex]y-y_1=m(x-x_1)\\y-(-4)=\frac{-1}{10}(x-(-1))\\y+4=\frac{-1}{10}(x+1)[/tex]
So, the equation in point-slope form is: [tex]y+4=\frac{-1}{10}(x+1)[/tex]
