Answer
The equation of a line passing through two given points can be found using the slope-intercept form, which is y = mx + b.
To find the slope (m) of the line, we use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two given points.
Given the points (-8, 3) and (-2, 0), we can calculate the slope as follows:
m = (0 - 3) / (-2 - (-8))
= -3 / 6
= -1/2
Now, we have the slope (m) as -1/2.
Next, we can substitute one of the given points and the slope into the slope-intercept form to find the y-intercept (b). Let's use the point (-8, 3):
3 = (-1/2)(-8) + b
Simplifying the equation, we get:
3 = 4 + b
Subtracting 4 from both sides:
b = -1
Therefore, the y-intercept (b) is -1.
Now, we have the slope (m) as -1/2 and the y-intercept (b) as -1. We can substitute these values back into the slope-intercept form to obtain the equation of the line:
y = (-1/2)x - 1
Hence, the equation of the line passing through the points (-8, 3) and (-2, 0) is y = (-1/2)x - 1.