Question

Consider the equation 5x+6y=−12. A line parallel to the above line would have a slope of

a) 5/6
b) -6/5
c) -5/6
d) 6/5

Answer 1

The slope of the line given by the equation 5x + 6y = -12 is -5/6. Therefore, the slope of a line parallel to this line would also be -5/6, which is option c).

Step-by-step explanation:

Finding the Slope of a Parallel Line

To find the slope of a line parallel to the line given by the equation 5x + 6y = -12, we first need to rewrite the equation in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Since parallel lines have the same slope, we'll identify the slope of the original line and that will be the slope of any line parallel to it.

Let's rearrange the original equation to solve for y:

1. 5x + 6y = -12
2. 6y = -5x - 12
3. y = (-5/6)x - 2

The slope of this line is -5/6, so the slope of any line parallel to this one would also be -5/6, which corresponds to option c).