Final answer:
The resulting equation is y = x - 6.
Step-by-step explanation:
To find the linear equation for the two points (-3,-9) and (4, -2), we first need to determine the slope (m) of the line that connects these points. The slope is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are coordinates of the two points.
Applying the formula, we get:
m = (-2 - (-9)) / (4 - (-3))
m = (7) / (7)
m = 1
Now that we have the slope, we'll use point-slope form (y - y1) = m(x - x1) to create the equation, and for this example, we'll use the first point (-3, -9).
The equation becomes:
y - (-9) = 1(x - (-3))
y + 9 = x + 3
By simplifying, we get the equation in slope-intercept form (y = mx + b):
y = x - 6
This is the linear equation that represents the line passing through the points (-3, -9) and (4, -2).