Question

look at this graph.
what is the equation of the line in slope - intercept form?
write your answer using integers, proper fractions, and improper fractions in simplest form.
y = \square

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, -1)\) (the y - intercept) and another point, say \((1, -3)\) (we can also use other points, for example, when \(x = 0\), \(y=- 1\); when \(x = 1\), \(y=-3\)).

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 \((x_2,y_2)=(1, - 3)\). Then \(m=\frac{-3-(-1)}{1 - 0}=\frac{-3 + 1}{1}=\frac{-2}{1}=-2\).

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 \(m=-2\) and from the point \((0,-1)\), the y - intercept \(b=-1\). So the equation of the line is \(y=-2x-1\).

Answer:

\(y=-2x - 1\)