Question

write the equation of the line in fully simplified slope-intercept form.

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, -4)\) (the y - intercept) and another point, for example, \((1, -5)\).

Step2: Calculate the slope (\(m\))

The formula for slope between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((0, - 4)\) as \((x_1,y_1)\) and \((1, - 5)\) as \((x_2,y_2)\), we have \(m=\frac{-5-(-4)}{1 - 0}=\frac{-5 + 4}{1}=\frac{-1}{1}=-1\).

Step3: Use slope - intercept form (\(y=mx + b\))

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We know that \(m=-1\) and from the point \((0, - 4)\), \(b=-4\) (since when \(x = 0\), \(y=b\)). Substituting \(m=-1\) and \(b = - 4\) into the equation, we get \(y=-x-4\).

Answer:

\(y=-x - 4\)