Question

analytic geometry
which equation represents the linear function that is shown on the given graph?
$y = \frac{1}{2}x - 2$
$y = \frac{1}{2}x + 4$
$y = 4x - 2$
$y = - 2x + 4$

Explanation:

Step1: Find the slope ($m$)

Use the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points from the graph, say $(0,4)$ and $(1,2)$.
$$m=\frac{2 - 4}{1 - 0}=\frac{-2}{1}=-2$$

Step2: Find the y - intercept ($b$)

The y - intercept is the value of $y$ when $x = 0$. From the point $(0,4)$, $b = 4$.

Step3: Write the equation

The slope - intercept form of a line is $y=mx + b$. Substituting $m=-2$ and $b = 4$ gives $y=-2x + 4$.

Answer:

$y=-2x + 4$