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

1/14/2013 | Amy from Winter Park, FL | Answered

3 Answers | 0 Votes

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

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

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