Question

A given line has the equation (10x + 2y = -2). What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, -5)?

a) (y = -5x + 12)
b) (5x + y = 12)
c) (y - 12 = 5(2 - 0))
d) (5x + y = -1)

Answer 1

The slope of the given line is -5, so the parallel line must also have a slope of -5. Since it passes through (0, -5), the y-intercept is -5. Thus, the equation of the parallel line is y = -5x - 5, which doesn't match any of the provided options.

Correct option is not given .

Step-by-step explanation:

The equation of the given line is 10x + 2y = -2. To find the slope-intercept form, we solve for y:

2y = -10x - 2

y = -5x - 1

Here, the slope (m) is -5 and the y-intercept (b) is -1. Since parallel lines have the same slope, the slope of the line we are looking for is also -5. The line must pass through the point (0, -5), so this is its y-intercept.

Therefore, the equation of the line in slope-intercept form is:

y = -5x + (-5)

y = -5x - 5

Comparing this with the provided options, none of them directly match this equation, indicating a potential typo in the question.

However, if the question intended to have the expression 'y = -5x - 5' amongst the options, we would select it as the correct answer.

Correct option is not given .