Question

what is the equation of the graph below? (4 pts)
equation:

Explanation:

Step1: Identify slope - intercept form

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

Step2: Find the y - intercept

The line crosses the y - axis at the point $(0,5)$, so $b = 5$.

Step3: Calculate the slope

Using two points $(0,5)$ and $(5,3)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1 = 5,x_2 = 5,y_2 = 3$. Then $m=\frac{3 - 5}{5-0}=\frac{-2}{5}=-\frac{2}{5}$.

Step4: Write the equation

Substitute $m =-\frac{2}{5}$ and $b = 5$ into $y=mx + b$, we get $y=-\frac{2}{5}x + 5$.

Answer:

$y =-\frac{2}{5}x + 5$