Question

By comparing the given pair of lines' equations, determine if they intersect at a point, are parallel, or coincide.

[6x + 9y + 39 + 2 = 0]

[8x + 64 + 22 = 0]

a) Intersect at a point

b) Parallel

c) Coincide

Answer 1

The given pair of lines intersect at a point.

Step-by-step explanation:

The given pair of lines' equations are:

Line 1: 6x + 9y + 39 + 2 = 0

Line 2: 8x + 64 + 22 = 0

To determine if the lines intersect at a point, are parallel, or coincide, we need to analyze their slopes.

For Line 1, the equation can be rearranged to y = -(2/9)x - 5. Plotting this line on a graph, we can see that it has a slope of -2/9.

For Line 2, the equation can be rearranged to y = -8x - 86. Plotting this line on a graph, we can see that it has a slope of -8.

Since the slopes of the two lines are different, they intersect at a single point. Therefore, the correct answer is Intersect at a point.