Question

write the equation of this line in slope-intercept form.
write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Recall 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 the line also passes through $(5,0)$. The formula for slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,5)$ and $(x_2,y_2)=(5,0)$. Then $m=\frac{0 - 5}{5 - 0}=\frac{- 5}{5}=-1$.

Step4: Write the equation

Substitute $m=-1$ and $b = 5$ into the slope - intercept form $y=mx + b$. We get $y=-x + 5$.

Answer:

$y=-x + 5$