Question

problem 11: spiral review
these two lines are parallel.
write an equation for each line.
line a: $y = \frac{4}{5}x$
line b:
(graph with two lines, line a (blue) passing through (0,0) and (5,4), line b (green) passing through (0, -3.2) and other points, with some handwritten notes like 2.5, 2 on the graph)

Explanation:

Step1: Recall parallel lines have equal slopes

Since Line \(a\) and Line \(b\) are parallel, they have the same slope. The slope of Line \(a\) is \(\frac{4}{5}\), so the slope of Line \(b\) is also \(\frac{4}{5}\).

Step2: Identify the y-intercept of Line \(b\)

From the graph, Line \(b\) passes through the point \((0, -3.2)\). The y-intercept (\(b\)) of a line in the form \(y = mx + b\) is the value of \(y\) when \(x = 0\). So for Line \(b\), \(b=-3.2\) (or \(-\frac{16}{5}\)).

Step3: Write the equation of Line \(b\)

Using the slope-intercept form \(y = mx + b\), where \(m=\frac{4}{5}\) and \(b = - 3.2\) (or \(-\frac{16}{5}\)), the equation of Line \(b\) is \(y=\frac{4}{5}x-3.2\) (or \(y=\frac{4}{5}x-\frac{16}{5}\)).

Answer:

\(y = \frac{4}{5}x - 3.2\) (or \(y=\frac{4}{5}x-\frac{16}{5}\))