Answer:
First, we know that:
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
Then for line FG = f(x), we know that it passes through the points (4, 9) and (1, 3)
Then the slope is:
a = (9 - 3)/(4 - 1) = 6/3 = 2
f(x) = 2*x + b
To find the value of b we can use one of the points, i will use the point (1, 3)
this means that when x = 1, f(1) = 3.
Then:
f(1) = 3 = 2*1 + b
3 = 2 + b
3 - 2 = b = 1.
The line FG is f(x) = 2*x + 1.
For a general linear equation:
y = a*x + b
The equation for a perpendicular line is:
y = (-1/a)*x + c
We know that:
f(x) = 2*x + 1
The perpendicular line will be something like:
g(x) = (-1/2)*x + c
To find the value of c, we use the fact that this line passes through the point (2, 0), then:
g(2) = 0 = (-1/2)*2 + c
0 = -1 + c
1 = c
The line is: g(x) = (-1/2)*x + 1
