Question

Find the equation of the line with the given description.parallel to y = 3x − 4, passes through (5, 4)

Answer 1

Given the equation of a line:

$y=3x-4$

You can identify that it is written in Slope-Intercept Form:

$y=mx+b$

Where "m" is the slope of the line and "b" is the y-intercept.

By definition, parallel lines have the same slope but different y-intercepts. Therefore, you can determine that the slope of the given line and the slope of the line you must find is:

$m=3$

Because they are parallel.

You know that the other line passes through this point:

$(5,4)$

Then, you can set up:

$\begin{gathered} x=5 \\ y=4 \end{gathered}$

And substitute the slope and those coordinates into:

$y=mx+b$

Then, by substituting values into the equation and solving for "b", you get:

$\begin{gathered} 4=3(5)+b \\ 4=15+b \\ 4-15=b \\ b=-11 \end{gathered}$

Knowing the values of "m" and "b", you can write the equation of the other line in Slope-Intercept Form:

$y=3x-11$

Hence, the answer is:

$y=3x-11$