Question

these two lines are parallel. write an equation for each line. line a line b

Explanation:

Step1: Find slope of Line a (and Line b, since parallel)

Line a passes through \((0, 0)\) (y-intercept) and \((5, 4)\). Slope \(m = \frac{4 - 0}{5 - 0} = \frac{4}{5} = 0.8\).

Step2: Equation for Line a

Using slope - intercept form \(y = mx + b\), \(b = 0\) (passes through origin), so \(y = 0.8x\) or \(y=\frac{4}{5}x\).

Step3: Equation for Line b

Slope is same as Line a (\(m = 0.8\)), y - intercept \(b=-3.2\). So equation is \(y = 0.8x - 3.2\) or \(y=\frac{4}{5}x - \frac{16}{5}\).

Answer:

Line a: \(y = \frac{4}{5}x\) (or \(y = 0.8x\))
Line b: \(y = \frac{4}{5}x - 3.2\) (or \(y=\frac{4}{5}x-\frac{16}{5}\))