Answer:
[tex]\displaystyle y=\frac{1}{2}x-2[/tex]
Step-by-step explanation:
The equation of the line in slope-intercept form is:
y=mx+b
Being m the slope and b the y-intercept.
Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The points are (-6,-5) and (-4,-4), thus:
[tex]\displaystyle m=\frac{-4+5}{-4+6}=\frac{1}{2}[/tex]
Knowing the value of the slope, the equation of the line is:
[tex]\displaystyle y=\frac{1}{2}x+b[/tex]
The value of b can be found using any of the points in the equation and solving for b. Let's pick the point (-6,-5):
[tex]\displaystyle -5=\frac{1}{2}(-6)+b[/tex]
Operating:
-5=-3+b
Solving:
b=-2
The equation of the line is:
[tex]\boxed{\displaystyle y=\frac{1}{2}x-2}[/tex]
