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 \((0,-5)\), so \(b=-5\).

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

Use two points, e.g., \((0, - 5)\) and \((3,1)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute \(x_1 = 0,y_1=-5,x_2 = 3,y_2 = 1\) into the formula: \(m=\frac{1-(-5)}{3 - 0}=\frac{6}{3}=2\).

Step4: Write the equation

Substitute \(m = 2\) and \(b=-5\) into \(y=mx + b\), we get \(y = 2x-5\).

Answer:

\(y = 2x - 5\)