Answer:
The equation in point-slope form is: [tex]\mathbf{y+8= \frac{4}{9}(x+3)}[/tex]
Step-by-step explanation:
Write the equation of the line that passes through the points (-3,-8) and (6,-4)
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=-3, y_1=-8, x_2=6 \ and \ y_2=-4[/tex]
Putting values and finding slope
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-4-(-8)}{6-(-3)}\\Slope=\frac{-4+8}{6+3}\\Slope=\frac{4}{9}[/tex]
So, slope m = 4/9
Using point (-3,-8) and slope m = 4/9 the equation is:
[tex]y-y_1=m(x-x_1)\\y-(-8)=\frac{4}{9}(x-(-3))\\y+8= \frac{4}{9}(x+3)\\[/tex]
So, the equation in point-slope form is: [tex]\mathbf{y+8= \frac{4}{9}(x+3)}[/tex]
