Question

write the equation of the line in fully simplified slope-intercept form.

Explanation:

Step1: Identify slope-intercept form

Slope - intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step2: Find the y - intercept (\(b\))

The line crosses the y - axis at \((0,-1)\), so \(b=-1\).

Step3: Calculate the slope (\(m\))

We can use two points on the line. Let's take \((0, - 1)\) and \((5,0)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \(x_1 = 0,y_1=-1,x_2 = 5,y_2 = 0\) into the formula: \(m=\frac{0-(-1)}{5 - 0}=\frac{1}{5}\).

Step4: Write the equation

Substitute \(m=\frac{1}{5}\) and \(b = - 1\) into \(y=mx + b\). We get \(y=\frac{1}{5}x-1\).

Answer:

\(y=\frac{1}{5}x - 1\)