Question

Lime FG goes through the points (4,9) and (1,3). Which equation represents a line that is perpendicular to FG and passes through the point (2,0)

Answer 1

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