Determine the slopes of the following two lines and state if they are parallel, perpendicular or neither: 3x−10y−18=0 and −40x−12y−6=0 The slope of line 3x−10y−18=0 is m=

To determine the slope of a line in the form Ax + By + C = 0, we rewrite the equation in slope-intercept form y = mx + b, where m is the slope of the line.

For the line 3x - 10y - 18 = 0, we rearrange the equation to slope-intercept form:
3x - 10y - 18 = 0
-10y = -3x + 18
y = 3/10x - 9/5

The slope of the line is m = \frac{3}{10}.

Now, let's determine the slope of the line -40x - 12y - 6 = 0:
-40x - 12y - 6 = 0
-12y = 40x + 6
y = -\frac{10}{3}x - \frac{1}{2}

The slope of the second line is m = -\frac{10}{3}.

To determine if the two lines are parallel, perpendicular, or neither, we compare their slopes:
The slopes are \frac{3}{10} and -\frac{10}{3}.
Since the product of the slopes is (-1), the lines are perpendicular.

\boxed{Answer: Perpendicular}