Consider the following systems of equations:
y= .5x-1
y= .5x+4
Are the graphs of the two lines intersecting lines, the same line, or parallel lines?
How many solutions does the system have?
A) No solution: The lines are parallel because the y-intercept is the same.
B) One Solution: The lines are parallel because the slope is the same.
C) Infinite Solutions: The lines are intersecting because the line is in slope form.
D) No solution: The lines are parallel because their slope is the same.
Plz help.
since they have the same slope (.5) they are either parallel or the same line.
Now try to find any value of x which satisfies both equations ...
the general slope-intercept equation is ... y = m x + b ... m is the slope
lines with the same slope are parallel
thanks😊
To determine whether the graphs of the two lines are intersecting lines, the same line, or parallel lines, we need to compare their slopes and y-intercepts.
The given system of equations is:
y = 0.5x - 1
y = 0.5x + 4
First, let's compare the slopes of the two lines. The coefficient of x in both equations is 0.5, which means both lines have the same slope. This rules out options B and D.
Next, let's compare the y-intercepts of the two lines. The y-intercept of the first equation is -1, while the y-intercept of the second equation is +4. Since the y-intercepts are different, the lines cannot be the same line, which rules out option C.
Therefore, the correct answer is A) No solution: The lines are parallel because the y-intercept is the same.