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 \((0, 0)\) and \((1, -5)\) (we can also use other points like \((-1, 5)\) or \((-2, 10)\), but \((0,0)\) and \((1, -5)\) are easy to identify).

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

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(1, -5)\), we get \(m=\frac{-5 - 0}{1 - 0}=\frac{-5}{1}=-5\).

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

The slope - intercept form of a line is \(y = mx + b\). Since the line passes through the origin \((0,0)\), when \(x = 0\), \(y = 0\). Substituting \(x = 0\), \(y = 0\) and \(m=-5\) into \(y=mx + b\), we have \(0=-5(0)+b\), so \(b = 0\).

Step4: Write the equation

Substituting \(m=-5\) and \(b = 0\) into the slope - intercept form \(y=mx + b\), we get \(y=-5x+0\) or simply \(y=-5x\).

Answer:

\(y = - 5x\)