What is the equation of a line parallel to y=4/5x+2 that passes through (1,2)

Question

fudzisako · Accepted Answer

To find the equation of a line parallel to the line given by

y = \frac{4}{5} x + 2

that passes through the point (1, 2), we can use the fact that parallel lines have the same slope.
The given line has a slope of

\frac{4}{5}

. Since the parallel line has the same slope, the equation of the line we're looking for can be written as:

y = \frac{4}{5} x + b

where

b

is the y-intercept.
To determine the value of

b

, we substitute the coordinates of the point (1, 2) into the equation:

2 = \frac{4}{5} (1) + b

Simplifying:

2 = \frac{4}{5} + b

To isolate

b

, we subtract

\frac{4}{5}

from both sides:

2 - \frac{4}{5} = b

10 / 5 - 4 / 5 = b

6 / 5 = b

Now we have the value of

b

. The equation of the line parallel to

y = \frac{4}{5} x + 2

and passing through (1, 2) is:

y = \frac{4}{5} x + \frac{6}{5}

What is the equation of a line parallel