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 the points \((-1, 5)\) and \((1, -7)\) (we can also use other points like \((0, -1)\) but let's use these two for slope calculation).

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

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \(x_1=-1\), \(y_1 = 5\), \(x_2=1\), \(y_2=-7\) into the formula:
\(m=\frac{-7 - 5}{1-(-1)}=\frac{-12}{2}=-6\)

Step3: Determine the y - intercept (\(b\))

The slope - intercept form of a line is \(y=mx + b\). We can use the point \((0,-1)\) (from the graph, when \(x = 0\), \(y=-1\)) to find \(b\).
Substitute \(x = 0\), \(y=-1\) and \(m=-6\) into \(y=mx + b\):
\(-1=-6(0)+b\)
\(b=-1\)

Step4: Write the equation

Substitute \(m=-6\) and \(b = - 1\) into the slope - intercept form \(y=mx + b\):
\(y=-6x-1\)

Answer:

\(y=-6x - 1\)