Question

write the slope intercept form of the equation of the line.
equation: $y = -\frac{1}{2}x - 1$

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is given by the equation \(y=mx + b\), where \(m\) is the slope of the line and \(b\) is the \(y\) - intercept (the value of \(y\) when \(x = 0\)).

Step2: Identify the \(y\) - intercept

From the graph, the line crosses the \(y\) - axis at the point \((0,- 1)\). So, the \(y\) - intercept \(b=-1\).

Step3: Calculate the slope

To find the slope \(m\), we can use two points on the line. Let's take the \(y\) - intercept \((0,-1)\) and another point, for example, \((2,-2)\). The formula for slope between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

Substitute \(x_1 = 0,y_1=-1,x_2 = 2,y_2=-2\) into the slope formula:

\(m=\frac{-2-(-1)}{2 - 0}=\frac{-2 + 1}{2}=\frac{-1}{2}=-\frac{1}{2}\)

Step4: Write the equation

Now that we have \(m =-\frac{1}{2}\) and \(b=-1\), substitute these values into the slope - intercept form \(y=mx + b\).

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

Answer:

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