Question

Line a passes through the points (-3, -2) and (0, 4). Line b passes through the

points (-2,-3) and (0, 1). Tell whether each statement is True or False.
a. Lines a and b intersect.
b. Lines a and b have different slopes.
c. Lines a and b have different y-intercepts.
d. Lines a and b are parallel.

Answer 1

Answer: True: a,b,c

False: d

Step-by-step explanation: a. True. Lines a and b intersect at some point. To determine whether the intersection point is within the given line segments or not, further analysis is needed.

b. True. The slope of line a is (4 - (-2)) / (0 - (-3)) = 2, and the slope of line b is (1 - (-3)) / (0 - (-2)) = 2, so they have the same slope.

c. True. The y-intercept of line a can be found by substituting the coordinates of one of the points into the equation of the line: -2 = 2*(-3) + b, so b = 4. Therefore, the equation of line a is y = 2x + 4, and its y-intercept is 4. Similarly, the equation of line b is y = 2x - 1, so its y-intercept is -1. Therefore, lines a and b have different y-intercepts.

d. False. Since lines a and b have the same slope, they are not parallel.

Answer 2

a. True, the two lines intersect at point (2, 2).

b. True, the slope of line a is (4 - (-2)) / (0 - (-3)) = 2, and the slope of line b is (1 - (-3)) / (0 - (-2)) = 2/2 = 1.

c. True, the y-intercept of line a can be found by plugging in one of the points into the slope-intercept form of the line (y = mx + b): -2 = 2*(-3) + b, which gives b = 4. So the equation of line a is y = 2x + 4, which means the y-intercept is 4. The y-intercept of line b can be found similarly: -3 = 1*(-2) + b, which gives b = -1. So the equation of line b is y = x - 1, which means the y-intercept is -1. Since the y-intercepts are different, the lines have different y-intercepts.

d. False, the slopes of the two lines are different (as shown in part b), so the lines are not parallel.

Explanation: