What is an equation of the line that passes through the point left bracket, minus, 4, comma, minus, 6, right bracket(−4,−6) and is parallel to the line 5, x, minus, 2, y, equals, 25x−2y=2?

Answer 1

To find the equation of a line parallel to 5x - 2y = 2 and passing through the point (-4,-6), we first need to determine the slope of the original line. We can do this by rearranging the equation into slope-intercept form (y = mx + b), where m represents the slope:

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

The slope of the original line is 5/2.

Since the line we are looking for is parallel to this line, it will have the same slope. Thus, the slope of our new line is also 5/2.

Now we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting (-4,-6) for (x1,y1) and 5/2 for m, we have:

y - (-6) = (5/2)(x - (-4))

Simplifying:

y + 6 = (5/2)(x + 4)
y + 6 = (5/2)x + 10
y = (5/2)x + 10 - 6
y = (5/2)x + 4

Therefore, the equation of the line that passes through (-4,-6) and is parallel to 5x - 2y = 2 is y = (5/2)x + 4.