Question

what is the equation of the linear function? y = -\frac{1}{2}x + 6 y = -\frac{1}{2}x + 3 y = -2x + 3 y = \frac{1}{2}x + 3

Explanation:

Step1: Identify y - intercept

The line crosses the y - axis at $y = 3$, so the y - intercept $b=3$.

Step2: Calculate the slope

Pick two points, say $(0,3)$ and $(6,0)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 3}{6-0}=-\frac{1}{2}$.

Step3: Write the equation

The slope - intercept form of a line is $y=mx + b$. Substituting $m =-\frac{1}{2}$ and $b = 3$ gives $y=-\frac{1}{2}x+3$.

Answer:

$y =-\frac{1}{2}x + 3$