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 $(0,5)$, so $b = 5$.

Step3: Calculate the slope ($m$)

We can use two points on the line. We know the y - intercept is $(0,5)$ and another point, for example, when $x = 2$, $y = 0$ (the x - intercept). The formula for slope is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,5)$ and $(x_2,y_2)=(2,0)$. Then $m=\frac{0 - 5}{2 - 0}=\frac{- 5}{2}$.

Step4: Write the equation

Substitute $m =-\frac{5}{2}$ and $b = 5$ into the slope - intercept form $y=mx + b$. We get $y=-\frac{5}{2}x + 5$.

Answer:

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