Write an equation of the line that passes though point P and is parallel to the line with the given equation.

Question

P(-7,-4), y=16

 

and 

 

P(-2,1),10x+4y=-8

Answer 1

Hi Kim

 

For the first problem all we need to do is find the horizontal line that passes through the point (-7,-4) since we are dealing with a line that has constant slope and is strictly horizontal.

 

We need the equation of our line to go through the y coordinate of -4, therefore, the equation of our line parallel to        y = 16 and passing through (-7,-4) is y = -4.

 

The second problem is a little more difficult since we are dealing with a line that is not constant and horizontal.

 

First, we need our equation in slope intercept form ( y = mx + b).

 

The equation, in slope intercept form, after using basic algebra, is y = -5/2x - 2.

 

Now we use the formula (y - y₁) = m (x - x₁).

 

We use our information and substitute as follows:

 

(y - 1) = -5/2 (x - (-2)) ---> (y - 1) = -5/2 (x + 2)

 

We distribute the -5/2, which is the slope, to the x and the positive 2 (the 2 is positive because we are subtracting a negative, resulting in a positive).

 

(y - 1) = -5/2x - 5 ----> now add one to both sides...

 

y = -5/2x -4 - this is our equation of the line that is parallel to our original equation and passes through the point (-2,1)

Answer 2

P(-7,-4), y=16  This is a horizontal line, all horizontal lines are of the form y = b.   From the point, y = -4, so the line is y = -4.

 

P(-2,1),10x+4y=-8

 

For all lines parallel to given line are of form  10x + 4y = c.   Substituting the given point 10(-2) + 4(1) = c = -8.

 

So 10x + 4y = -8 is the equation of the line.