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: Identify slope-intercept form

Slope - intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. From the graph, the line crosses the y - axis at \((0,-1)\), so \(b=-1\).

Step2: Calculate the slope

We can use two points on the line. Let's take \((0, - 1)\) and \((2,-2)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1 = 0,y_1=-1,x_2 = 2,y_2=-2\) into the formula, we get \(m=\frac{-2-(-1)}{2 - 0}=\frac{-2 + 1}{2}=\frac{-1}{2}\).

Step3: Write the equation

Substitute \(m =-\frac{1}{2}\) and \(b=-1\) into the slope - intercept form \(y=mx + b\). So the equation is \(y=-\frac{1}{2}x-1\).

Answer:

\(y = -\frac{1}{2}x - 1\)