The slope of two parallel lines are equal. We shall begin by calculating the slope of the line y = 3x + 4.
Note that the slope of a line expressed in slope-intercept form (as given in the question) is the coefficient of x. The slope of this equation therefore is 3.
Given the points (3, 2), we solve as follows;
[tex]\begin{gathered} y=mx+b \\ \text{Substitute for the known values, that is x, y and m} \\ 2=3(3)+b \\ 2=9+b \\ 2-9=b \\ b=-7 \\ \text{Having the slope as 3, and the y-intercept as -7} \\ \text{The equation becomes;} \\ y=mx+b \\ y=3x+\lbrack-7\rbrack \\ y=3x-7 \end{gathered}[/tex]The equation of a parallel line that passes through (3, 2) is
y = 3x - 7
