Question

Ms. Rodriguez showed her students how to solve this system of equations.

y = 2x - 5
y = 2x - 1
She found that the lines were parallel. What does this mean?
A The graphs of the lines intersect at the point (-1,-5)
B That the graphs will never intersect.
C That the graphs have infinite solutions
D That the equations intersect the y-axis at 2.

Answer 1

Lines described by y = 2x - 5 and y = 2x - 1 are parallel lines , meaning they have the same slope but different y-intercepts and will never intersect.

Step-by-step explanation:

When Ms. Rodriguez found that the equations y = 2x - 5 and y = 2x - 1 were parallel, this means that the graphs of these lines will never intersect. In the context of linear equations and the algebra of straight lines, the slope of a line (m) indicates how steep the line is, and the y-intercept (b) indicates where it crosses the y-axis.

Since both equations have the same slope (2) but different y-intercepts (-5 and -1), this means that the lines are parallel to each other and will maintain the same distance apart indefinitely without crossing.

Therefore it will have y-intercepts and will never intersect.