Question

y = f(x)The graph of the linear function f is shown in thexy-plane above. The graph of the linear function g(not shown) is perpendicular to the graph offand passes throu the point (1,3). What is thevalue of g(0)?

Answer 1

Answer : its c

Explanation

Answer 2

g(0) = 5/2

Explanation:

The equation of a line is given by:

y = ax + b

In which a is the slope, which is given by the variation in y divided by the variation in x.

If two lines are perpendicular, the multiplication of their slopes is -1.

Line f:

Passes through the points (0,3) and (1,1).

Variation in y: 1 - 3 = -2

Variation in x: 1 - 0 = 1

Slope = -2/1 = -2.

Line g:

Perpendicular to g, so the slope is:

-2*a = -1

2a = 1

a = 1/2

So the line g has an equation given by:

y = (1/2)*x + b

Passes through the point (1,3).

This means that when x = 1, y = 3. We use this to find b.

3 = (1/2)*1 + b

b = 3 - 1/2

b = 5/2

So:

g = y(x) = (1/2)*x + 5/2

g(0) = (1/2)*0 + 5/2 = 5/2

g(0) = 5/2