Line L passes through (1,-5) and line P is the graph of y-2=-3(x+6). if L is parallel to P what isthe slope intercept form equation of L?

Question

Complete the equation of the line in slope intercept in slope intercept form

Answer 1

Let's first recall what it means to have lines that are parallel to each other.  Lines are parallel when their slopes are equal to each other.

 

Now let's work with line P to determine the slope of the line.  In slope-intercept form we get the slope very easily.  If slope-intercept form is y = mx + b, m is the slope.  Let's work with line P to put it into slope intercept form.  First distribute the -3, making the equation

 

y - 2 = -3x - 18

 

Then add 2 to both sides to get y by itself.  This leaves line P as 

 

y = -3x - 16

 

So now based on the slope-intercept form (bold above) we've determined that the slope = -3.

 

Now let's move to line L.  It has the same slope since the problem says the lines are parallel, therefore m = -3.  We are given a point, which we plug in for x and y respectively.  This makes line L

 

-5 = -3*1 + b

 

When we solve for b, we will have the slope-intercept form of the equation for line L.  Solving for b leaves us with b = -2, therefore the equation for line L is

 

y = -3x - 2