2x + 5y = 15. What is the equation of the parallel northbound track that runs through the point (4, – 2)?

Answer 1

Parallel, so the track must have the same slope as 2x+5y=15, 5y = 15 -2x, y = 3 - (2/3) x, slope = -2/3

So (y-y1)/ (x-x1) = m, where (x1,y1) = (4,-2) and m = -2/3

(y+2) / (x-4) = (-2/3).

You can rearrange this to get the final equation.

Answer 2

To answer this question, you would need to know a few things:

1) That parallel lines have the same slope.

2) How to find the slope of a given line.

3) How to use that slope and a point to get the equation for a new line.

Keeping number 1 in mind, you would want to take the equation given and solve for y so that your equation is in slope-intercept form (y = mx + b)

Once it is in slope-intercept form, you can see what the slope of that line is by looking at the "m" (the co-efficient of x, which tells us the slope.)

With this slope, you can use point slope form: (y - y₁) = m (x - x₁) using the point (4, -2) as your (x₁ , y₁)

This will give you the equation for a line that has the same slope as the line given and goes through the point (4, -2). Unless asked to put it in a specific final form, such as slope intercept or standard form, you would be done.