Question

graph the line that passes through the points (0, -8) and (5, -5) and determine the equation of the line.

Explanation:

Step1: Find the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \((x_1, y_1)=(0, -8)\) and \((x_2, y_2)=(5, -5)\). So, \(m=\frac{-5 - (-8)}{5 - 0}=\frac{-5 + 8}{5}=\frac{3}{5}\).

Step2: Identify the y-intercept (b)

The y-intercept is the value of y when \(x = 0\). From the point \((0, -8)\), when \(x = 0\), \(y=-8\), so \(b=-8\).

Step3: Write the equation of the line

The slope - intercept form of a line is \(y=mx + b\). Substituting \(m=\frac{3}{5}\) and \(b = - 8\) into the formula, we get \(y=\frac{3}{5}x-8\).

Answer:

The equation of the line is \(y=\frac{3}{5}x - 8\)