Question

PLEASE HELP ASAP PLEASE

Answer 1

Answer:

The equation that represents the line passing through the point (2, -4) with a slope of one half is

$f(x) = \frac{1}{2}x - 5$

Step-by-step explanation:

The equation of a line can be described by a first order equation in the following format:

$f(x) = ax + b$

In which a is the slope of the line.

Solution:

The line slope is $\frac{1}{2}$, so $a = \frac{1}{2}$.

The equation of the line now is:

$f(x) = \frac{1}{2}x + b$

The problem states that the line passes through the point(2,-4). This means that when x = 2, f(x) = -4

So:

$f(x) = \frac{1}{2}x + b$

$-4 = \frac{1}{2}*(2) + b$

$-4 = 1 + b$

$b = -5$

So, the equation that represents the line passing through the point (2, -4) with a slope of one half is

$f(x) = \frac{1}{2}x - 5$