Question

Find the equation of the line through (7,2) which is parallel to the line y=-3x-2

Answer 1

The general slope-intercept form of the line: y = m * x + b

The parallel lines have the same slope

Given the equation of the line: y= -3x - 2

the slope of the given line = -3

The required line is parallel to the given line

So, the slope of the required line = m = -3

The equation of the line will be: y = -3x + b

The required line passes through the point (7, 2)

So, when x = 7, y = 2

We will find the value of b as follows:

`\begin{gathered} 2=-3\cdot7+b \\ 2=-21+b \\ b=2+21=23 \end{gathered}`

So, the answer will be the equation of the line is:

`y=-3x+23`