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 $(0,1)$, so $b = 1$.

Step3: Calculate the slope ($m$)

We can use two points on the line. Let's use the y - intercept $(0,1)$ and the x - intercept $(3,0)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Substitute $x_1 = 0,y_1 = 1,x_2=3,y_2 = 0$ into the formula:
$m=\frac{0 - 1}{3 - 0}=\frac{- 1}{3}=-\frac{1}{3}$

Step4: Write the equation

Substitute $m =-\frac{1}{3}$ and $b = 1$ into the slope - intercept form $y=mx + b$.
We get $y=-\frac{1}{3}x + 1$

Answer:

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