Question

Given the following lines, which statement is true?

Line 1: y = -x - 3
Line 2: y = -2x + 4
Line 3: y = -x + 9
Line 4: y = -2x - 2
A) Line 1 and Line 3 are parallel.
B) Line 2 and Line 4 are perpendicular.
C) Line 2 and Line 4 intersect at the same point.
D) Line 3 has the steepest slope.

Answer 1

The true statement for the given lines is that Line 1 and Line 3 are parallel, both having a slope of -1, which means they share the same slope and therefore never intersect.

Step-by-step explanation:

The statement that is true regarding the given lines is that Line 1: y = -x - 3 and Line 3: y = -x + 9 are parallel. The slope of a line in the slope-intercept form (y = mx + b) is represented by the coefficient of x, which is m. If two lines are parallel, they have the same slope. Line 1 and Line 3 both have a slope of -1, which means they are parallel, making option A) correct.

Line 2: y = -2x + 4 and Line 4: y = -2x - 2 also have the same slope of -2, meaning they are parallel to each other, not perpendicular, thus option B) is incorrect. Option C) is incorrect because while Line 2 and Line 4 are parallel, they do not intersect at a point. Lastly, option D) is incorrect because the steepest slope among the given lines is -2 (belonging to Line 2 and Line 4), not -1 (the slope of Line 3).