Answer:
y = (-2/3)x + 6
Explanation:
To find the equation of the line that passes through the points (-3, 8) and (6, 2), we can use the slope-intercept form of the equation of a line, which is:
y = mx + b
where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.
To find the slope of the line, we can use the following formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line. Plugging in the coordinates of the two points given in the problem, we get:
m = (2 - 8) / (6 - (-3)) = -6/9 = -2/3
Next, we need to find the y-intercept of the line. This is the point where the line crosses the y-axis, which means that the x-coordinate of this point is 0. Since we know the slope of the line and one of the points that it passes through, we can use the point-slope form of the equation of a line to find the y-intercept:
y - y1 = m(x - x1)
Substituting the values we have calculated above and setting x = 0, we get:
y - 8 = (-2/3)(0 - (-3))
Solving for y, we find that the y-intercept is 8 - (2/3) * 3 = 8 - 2 = 6.
Therefore, the equation of the line that passes through the points (-3, 8) and (6, 2) is:
y = (-2/3)x + 6