The graph of the linear function f is shown in the xy-plane above. The graph of the linear function g (not shown) is perpendicular to the graph of f and passes through the point (1, 3). What is the value of g(0)?

The correct answer is: 7

○        The concept used in this question is the concept of lines.
○        Equation of line is given by y = mx + c
Where y is y-coordinate, x is x-coordinate and c is the y-intercept (the point at which the line crosses the y -axis).
○        The slope of the line is the angle it makes with the x-axis i.e θ
○        The slope of line m is tan θ.

• Step by step explanation:

○        Given:

1. The line lies in the xy plane.
2. The line has a slope of 2, i.e m = 2
3. The line passes through the point (0,3)

○        Step 1:
○        Let f(x) = mx + c
○        g(x) = m₂x + c₂
Find linear equation
According to the given graph,
The f(x) passes through (0,3) and (1,1),
 We know that the two point form equation of line lies in xy plane is given by,

So, according to the given information,
line passes through the point (1, 1) and (0,3)



m = 2
○        Step 2:
Also, it is given that g(x) is perpendicular to f(x)
∴ slope of f(x)   slope of g(x) = -1




○        Step 3:
Now, g(x) passes through (1,3).
Therefore (1,3) satisfy, g(x) = m₂x + c₂




∴ c₂ = 7
○        Step 3:
Now, put values in g(x)
g(x) = m₂x + c₂

• Final Answer:

Hence, the g(0) = 7.