Question

2 Write an equation of the line parallel to y = 3x + 7 going through the point (2,5). Equation of new line is

Answer 1

The Slope-Intercept form of the equation of a line is:

$y=mx+b$

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

In this case, you have the following equation of a line, which is written in Slope-Intercept form:

$y=3x+7$

You can identify that:

$\begin{gathered} m=3 \\ b=7 \end{gathered}$

By definition, the slopes of parallel lines are equal. Then, the slope of the other line is:

$m=3$

Knowing that this line passes through this point:

$(2,5)$

You can substitute the slope and the coordinates ot the given point into the following equation, and then solve for "b":

$y=mx+b$

Then, "b" is:

$\begin{gathered} 5=3(2)+b \\ 5=6+b \\ 5-6=b \\ b=-1 \end{gathered}$

Knowing the slope and the y-intercept, you get that the equation of the new line is:

$y=3x-1$