Write the equation of the linear function that passes through the points (
1
1,
5
5) and (
−
4
−4,
3
3).
First, we need to find the slope of the line using the given points.
Slope (m) = (y2 - y1) / (x2 - x1)
Slope (m) = (3 - 5) / (-4 - 1)
Slope (m) = -2 / -5
Slope (m) = 2/5
Now that we have the slope, we use one of the points to find the y-intercept.
Using point (1, 5):
5 = (2/5) * 1 + b
5 = 2/5 + b
b = 5 - 2/5
b = 25/5 - 2/5
b = 23/5
Therefore, the equation of the linear function is:
y = 2/5 x + 23/5