Question

Write an equation (in y-form) or the line that is parallel to y = -3x + 1 and contains (4, 2)

Answer 1

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

$y = mx + b$

Where:

m: It's the slope

b: It is the cut-off point with the y axis

By definition, if two lines are parallel then their slopes are equal. A line parallel to$y = -3x + 1$, will have the same slope -3. Thus, the equation will be of the form:

$y = -3x + b$

We substitute the given point and find "b":

$2=-3(4)+b\\2=-12+b\\2+12=b\\b=14$

Finally, the equation is:

$y = -3x + 14$

Answer:

$y = -3x + 14$