Question

write the equation of the line in fully simplified slope-intercept form.

Explanation:

Step1: Identify slope-intercept form

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

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

The line crosses the y-axis at $(0, 3)$, so $b = 3$.

Step3: Calculate the slope ($m$)

Use two points, e.g., $(0, 3)$ and $(8, 1)$. The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$.
Substituting values: $m = \frac{1 - 3}{8 - 0} = \frac{-2}{8} = -\frac{1}{4}$.

Step4: Write the equation

Substitute $m = -\frac{1}{4}$ and $b = 3$ into $y = mx + b$:
$y = -\frac{1}{4}x + 3$

Answer:

$y = -\frac{1}{4}x + 3$