Answer:
y = 4
Explanation:
To find the y-intercept of the line passing through the points (-6, -5), (-4, -2), (-2, 1), we need to first find the equation of the line.
We can use the point-slope form of the equation of a line, which is:
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is one of the given points.
First, we can find the slope of the line using two of the given points, say (-6, -5) and (-4, -2).
The slope, m, is given by:
m = (y2 - y1) / (x2 - x1) = (-2 - (-5)) / (-4 - (-6)) = 3/2
Now, we can use the point-slope form with the point (-6, -5):
y - (-5) = (3/2)(x - (-6))
y + 5 = (3/2)(x + 6)
y + 5 = (3/2)x + 9
y = (3/2)x + 4
So the equation of the line passing through the points (-6, -5), (-4, -2), (-2, 1) is y = (3/2)x + 4.
To find the y-intercept, we can set x = 0 in the equation:
y = (3/2)(0) + 4
y = 4
Therefore, the y-intercept of the line passing through the points (-6, -5), (-4, -2), (-2, 1) is 4.