Answer:
The equation that represents the line passing through the point (2, -4) with a slope of one half is
[tex]f(x) = \frac{1}{2}x - 5[/tex]
Step-by-step explanation:
The equation of a line can be described by a first order equation in the following format:
[tex]f(x) = ax + b[/tex]
In which a is the slope of the line.
Solution:
The line slope is [tex]\frac{1}{2}[/tex], so [tex]a = \frac{1}{2}[/tex].
The equation of the line now is:
[tex]f(x) = \frac{1}{2}x + b[/tex]
The problem states that the line passes through the point(2,-4). This means that when x = 2, f(x) = -4
So:
[tex]f(x) = \frac{1}{2}x + b[/tex]
[tex]-4 = \frac{1}{2}*(2) + b[/tex]
[tex]-4 = 1 + b[/tex]
[tex]b = -5[/tex]
So, the equation that represents the line passing through the point (2, -4) with a slope of one half is
[tex]f(x) = \frac{1}{2}x - 5[/tex]
