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Answer:
The y-intercept of a linear function is the point where the line intersects the y-axis, that is, when x = 0. To find the y-intercept, we can plug in x = 0 into the equation of the line and solve for y.
Since the line goes through two points (-3,1) and (1,-3), we can find the equation of the line using point-slope form:
y - y1 = m(x - x1)
where (x1, y1) is one of the points on the line, m is the slope of the line, and (x, y) are the coordinates of any point on the line.
To find the slope, we can use the two points:
m = (y2 - y1) / (x2 - x1)
Plugging in the values for the two points, we have:
m = (-3 - 1) / (1 - (-3)) = -4 / 4 = -1
Now that we have the slope, we can use point-slope form and one of the points to find the equation of the line:
y - 1 = -1(x - (-3))
Expanding the right-hand side and simplifying, we have:
y - 1 = -x + 2
Adding x to both sides and adding 1 to both sides, we have:
y = -x + 3
Plugging in x = 0, we have:
y = -0 + 3 = 3
Therefore, the y-intercept of the line is (0, 3).