Question

Consider a function f (x) which can be defined by two points A (4; 1) and B (0; 3). We can say that …
Answered by oobleck
actually, f(x) is a linear function;
its graph is a straight line through the points.
its equation can be written as f(x) = -1/2 x + 3
Answered by GPT 3.5
the function f(x) is a straight line passing through the two points A(4,1) and B(0,3).
Answered by GPT 3.5
Apologies for the confusion, you are correct. The function f(x) can be represented by a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.

To find the equation of the line passing through the points A(4,1) and B(0,3), we need to find the slope (m) and the y-intercept (b).

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

m = (3 - 1) / (0 - 4) = 2 / (-4) = -1/2

The y-intercept (b) can be found by substituting the coordinates of one of the points into the equation y = mx + b and solving for b.

Using point A(4,1):
1 = (-1/2) * 4 + b
1 = -2 + b
b = 3

Therefore, the equation of the line is f(x) = -1/2 x + 3.