Final answer:
The equation of the line passing through the points (-6,5) and (-3,-3) is y = (-8 / 3)x - 11.
Step-by-step explanation:
To find the equation of the line passing through the points (-6,5) and (-3,-3), we need to determine the slope (m) first, which is calculated by taking the difference in the y-coordinates and dividing it by the difference in the x-coordinates:
m = (y2 - y1) / (x2 - x1) = (-3 - 5) / (-3 - (-6)) = -8 / 3
Now that we have the slope, we can use the point-slope form to write the equation of the line. We'll use one of the given points, such as (-6,5), and the slope we found:
y - y1 = m(x - x1)
Plugging in the values, we get:
y - 5 = (-8 / 3)(x + 6)
To express this in slope-intercept form (y = mx + b), we need to distribute the slope and move the constant term to the other side of the equation:
y = (-8 / 3)x - (8 / 3)(6) + 5
After simplifying, we get:
y = (-8 / 3)x - 48 / 3 + 15 / 3 = (-8 / 3)x - 33 / 3
Therefore, the equation of the line is:
y = (-8 / 3)x - 11