Choose the equation of the line passing through the point (2, 6) and parallel to y = -3x - 4.

Question

I need help with this problem 

Answer 1

Two different lines are parallel if they have the same slope.

The slope of the line y = -3x - 4 is -3.

Using the point-slope form of the equation of a line gives

y - 6 = -3(x - 2) .

The slope-intercept form is y = -3x + 12.

Another way to solve the problem is let y = -3x + b and determine b from the given point.

Answer 2

Amy,

Parallel lines have the same slope.  So you need to find a line with the same slope as the given line (y=-3x-4), and that goes through the point (2,6).  The equation for your given line is in slope-intercept (y=mx+b) form, so finding the slope m is straightforward.  If you need help calculating the equation for a line given a point and the line's slope, I'd be happy to answer a follow-up question.  John

Answer 3

 

Parallel lines have the same slope.  To find the slope of the line they gave you, put the equation into slop-intercept form.  This is  y = mx + b.  y = -3x - 4.  Oh look - that equation is already in slope-intercept form!  The slope is the co-efficient of x.  (The number multiplying x)  So our slope is m = -3.

 

Start with y = mx + b and substitute in what you know.  x = 2, y = 6 and m = -3.

 

y = mx + b

6 =-3(2) +b            substitution

6 = -6 + b              multiplication

6 + 6 = -6 + 6 +b   added 6 to both sides

12 = 0 + b              combined like terms

12 = b

 

Now, you know the slope (m = -3) and the y-intercept (b = 12).  Use the slope-intercept form again...

 

y = mx + b

y = -3x + 12