Question

What do the following two equations represent?

· y = 6x-2
. 2x12y = 24
Choose 1 answer:
The same line
Distinct parallel lines
Perpendicular lines
Intersecting, but not perpendicular lines

Answer 1

The equations "y = 6x-2" and "2x + 12y = 24" do not represent the same line, but they do represent intersecting lines.

To see this, we can rewrite the second equation in slope-intercept form by solving for y:

2x + 12y = 24

12y = -2x + 24

y = (-1/6)x + 2

Now we can compare the slopes of the two equations. The slope of "y = 6x-2" is 6, while the slope of "y = (-1/6)x + 2" is -1/6. Since the slopes are not equal, the equations do not represent the same line.

However, we can see that the two lines do intersect at some point. To find this point, we can set the two equations equal to each other:

6x-2 = (-1/6)x + 2

Simplifying this equation, we get:

6x + (1/6)x = 4

(37/6)x = 4

x = (24/37)

Now we can substitute this value of x into either equation to find the corresponding value of y. Using "y = 6x-2", we get:

y = 6(24/37) - 2

y = (72/37)

Therefore, the two equations represent intersecting, but not perpendicular lines.