Final answer:
To find the equation of a linear function that passes through two given points, we need to determine the slope and the y-intercept of the line. Given the points (1, 3) and (-1, 5), the equation of the linear function is y = -x + 4.
Step-by-step explanation:
To find the equation of a linear function that passes through two given points, we need to determine the slope and the y-intercept of the line.
Given the points (1, 3) and (-1, 5), we can use the formula for slope:
m = (y2 - y1) / (x2 - x1)
Plugging in the values:
m = (5 - 3) / (-1 - 1) = 2 / -2 = -1
Now, we can use the point-slope form of the equation:
y - y1 = m(x - x1)
Choosing one of the points, let's use (1, 3):
y - 3 = -1(x - 1)
Simplifying the equation, we get:
y - 3 = -x + 1
y = -x + 4
Therefore, the equation of the linear function is y = -x + 4.