Question

find the equation in the form y = mx + b or x = c of the line pictured below.
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Explanation:

Step1: Find two - point coordinates

The line passes through (-5, 1) and (0, - 4).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(-5,1)\) and \((x_2,y_2)=(0,-4)\). Then \(m=\frac{-4 - 1}{0-(-5)}=\frac{-5}{5}=-1\).

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

The equation of a line is \(y = mx + b\). We know \(m=-1\) and the line passes through (0, - 4). Substituting \(x = 0\), \(y=-4\) and \(m=-1\) into \(y=mx + b\), we get \(-4=-1\times0 + b\), so \(b=-4\).

Step4: Write the equation of the line

The equation of the line is \(y=-x - 4\).

Answer:

\(y=-x - 4\)