Question

# The line y=4/5x+2 passes through (1,2). Express a line parallel to it with an equation.

Transformations of functions
The line $$\displaystyle{y}=\frac{{4}}{{5}}{x}+{2}$$ passes through (1,2)
Express a line parallel to it with an equation.

2021-09-10

$$y=mx+b$$
The lines are parallel when their m (slope) is the same.
$$\displaystyle{m}=\frac{{4}}{{5}}$$
Find b by substituting $$\displaystyle{m}=\frac{4}{{5}}$$ and $$(1,2)$$:
$$\displaystyle{2}=\frac{{4}}{{5}}{\left({1}\right)}+{b}$$
$$\displaystyle{2}=\frac{{4}}{{5}}+{b}$$
$$\displaystyle{b}=\frac{{6}}{{5}}$$
Thus, the expression is:
$$\displaystyle{y}=\frac{{4}}{{5}}{x}+\frac{{6}}{{5}}$$