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 \((0, 1)\) and \((1, -4)\) (we can also use other points, but these are easy to identify).

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 \((x_1, y_1)=(0, 1)\) and \((x_2, y_2)=(1, -4)\), we get:
\(m=\frac{-4 - 1}{1 - 0}=\frac{-5}{1}=-5\)

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

The slope - intercept form of a line is \(y = mx + b\), where \(b\) is the y - intercept (the value of \(y\) when \(x = 0\)).
We know that when \(x = 0\), \(y = 1\) (from the point \((0, 1)\)), so \(b = 1\).

Step4: Write the equation in slope - intercept form

Substituting \(m=-5\) and \(b = 1\) into \(y=mx + b\), we get:
\(y=-5x + 1\)

Answer:

\(y = - 5x+1\)