Line B, with the equation y = -2x - 1, is not congruent to Line A (y = 2x + 3) because it has a different slope and y-intercept. No line presented in the question is congruent to Line A.
To determine if any line is congruent to Line A, which has an equation of y = 2x + 3, we need to look for a line that has both the same slope and y-intercept as Line A. According to the definition, congruent lines have identical slopes and y-intercepts. Since Line A has a slope (m) of 2 and a y-intercept (b) of 3, we need another line with these exact same characteristics.
Line B is represented by the equation y = -2x - 1. Analyzing this, we see that Line B has a slope of -2 and a y-intercept of -1. The slope of Line B is the negative reciprocal of Line A, and the y-intercepts are also different. Therefore, based on their equations, Line B is not congruent to Line A because they do not share the same slope or y-intercept as required for congruency in lines.
Recall that slope is the steepness of a line and is consistent throughout its entire length (rise over run). The y-intercept is where the line crosses the y-axis. Since no other lines are given in the problem, we can conclude that no provided line is congruent to Line A.
The probable question may be:
In a math class, students are exploring congruent lines. Line A is represented by y=2x+3, and Line B is represented by y=−2x−1. Determine which line is congruent to Line A based on their equations.
Additional Information:
In the world of mathematics, congruent lines have the same slope and y-intercept. Line A has a slope of 2 and a y-intercept of 3. Meanwhile, Line B boasts a slope of −2 and a y-intercept of −1. As you explore these equations, remember that the slope is like the steepness of a line, and the y-intercept is where it crosses the y-axis. Which line aligns with Line A's characteristics, and thus, is congruent to it?