Which best describes the relationship between the lines with equations 8x+y=6 and 16x+2y=0

(a) perpendicular
(b) parallel
(c) same line
(d) neither parallel nor perpendicular

compare slopes

Which beat describes the relationship between the lines with equations 5x + y=4 and 20x + 4y = 16 ?

To determine the relationship between the two lines with equations 8x+y=6 and 16x+2y=0, we need to compare the slopes of the lines.

The given equations are in the general form Ax + By = C, where A, B, and C are constants. By rewriting the equations in slope-intercept form (y = mx + b), we can determine their slopes.

For the equation 8x + y = 6:
Subtract 8x from both sides: y = -8x + 6
This equation is in slope-intercept form (y = mx + b), where the coefficient of x (-8) is the slope of the line.

For the equation 16x + 2y = 0:
Subtract 16x from both sides: 2y = -16x
Divide both sides by 2: y = -8x
This equation is also in slope-intercept form (y = mx + b), where the coefficient of x (-8) is the slope of the line.

Comparing the slopes, we can see that both lines have the same slope (-8). Therefore, the correct answer is (c) they represent the same line.