P(-9,1), y+9x=-19

Question

Write the equation of the line that passes through the given point and is parallel to the given line.  Answer should be in slope intercept form

Answer 1

Given:

 

Point is (-9,1) 

y=-9x-19

 

 

Use the formula:  

 

y=mx+b

 

Substitute the given x and y values into this formula:

 

1=-9(-9)+b

 

Solve for b:

 

1=81+b

-80=b

 

Rewrite the formula and plug in b while removing the x and y values:

 

y=-9x-80

 

We can check by graphing the two lines.  The line that is obtained should pass through P(-9,1)

Answer 2

• First, let's rearrange the equation we have into slope intercept form (although a slick student won't need to)
• y=-9x-19
• m=-9 (this is the slope of the first line AND our new line, as parallel lines have the same slope)
• y-y₁=m(x-x₁)  This is the handy point slope formula that gets used a lot in high school math
• y-1=-9(x--9)  We are just putting the slope we have from the first line, with the point we are interested in, into this point-slope equation.
• y-1=-9(x+9)
• y-1=-9x-81
• y=-9x-80