Question

Line l passes through point (-4,47) and line p is the graph of y+1=-5(x+5). If l is parallel to p what is the equation of l?

Answer 1

`y _( \rm parallel) = - 5x +27`

Explanation:

The equation of line p is in point-slope form , that's

`y-y_1=m(x-x_1)`

Where:

• m is the slope
• 
  `(x_1,y_1)` is a point that lies on the line

Since line I is parallel to the line p , line I has the same slope as p. From the given equation of p , we can consider the slope of line p -5. Hence the slope of line I is also -5.

Now To determine the equation of I.

1. Use the point-slope form
2. plugin the value of m and
   `(x_1,y_1)` to the equation
3. simplify it to the slope intercept form.

We have

• 
  `(x_1,y_1)` =(-4,47)
• 
  `m_(parallel)=-5`

So, the equation of line l is

`y - 47 = - 5(x - ( - 4)) \\ \implies y - 47 = - 5 x- 20 \\ \implies \boxed{y _( \rm parallel) = - 5x + 27}`

And we're done!