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: Find two points on the line

We can see the line passes through (0, - 1) and (2,0).

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,-1)$ and $(x_2,y_2)=(2,0)$. Then $m=\frac{0 - (-1)}{2 - 0}=\frac{1}{2}$.

Step3: Identify the y - intercept $b$

The y - intercept is the y - coordinate of the point where the line crosses the y - axis. The line crosses the y - axis at (0, - 1), so $b=-1$.

Step4: Write the equation in slope - intercept form

The slope - intercept form is $y = mx + b$. Substituting $m=\frac{1}{2}$ and $b = - 1$ gives $y=\frac{1}{2}x-1$.

Answer:

$y=\frac{1}{2}x - 1$