The line can be written as y = (-5/2)*x - 1 and the graph is in the image at the end.
How to find the equation of the line?
A linear equation that passes through two points (x₁, y₁) and (x₂, y₂) has a slope given by:
a = (y₂ - y₁)/(x₂ - x₁)
Here the two points are (-2, -6) and (4, 9), then the slope is:
a = (9 +6)/(4 + 2)
a = 15/6 = 5/2
Then we can write:
y = (5/2)x + b
To find the value of b, we can replace the values of the first point (-2, -6)
-6 = (5/2)*-2 + b
-6 = -5 + b
-6 + 5 = b
-1 = b
The line is y = (-5/2)*x - 1
To graph the line, just plot the two given points and draw a line that passes through both of them.