Question

write an equation of the line below.

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through the points \((-1, 6)\) and \((0, -1)\) (we can also use \((0, -1)\) and another point, but let's use these two for calculation).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(-1,6)\) and \((x_2,y_2)=(0, - 1)\). Then \(m=\frac{-1 - 6}{0-(-1)}=\frac{-7}{1}=-7\).

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

The y - intercept is the value of \(y\) when \(x = 0\). From the point \((0,-1)\), we can see that \(b=-1\).

Step4: Write the equation in slope - intercept form

The slope - intercept form of a line is \(y=mx + b\). Substituting \(m=-7\) and \(b = - 1\) into the formula, we get \(y=-7x-1\).

Answer:

\(y = - 7x-1\)