if a system of linear equations has infinitely many solutions, what does this mean about the two lines?
1 answer:
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Answer:
D. y = 3/5x + 13/5
Step-by-step explanation:
The slope of the desired line is the ratio of the difference in y-values to the difference in x-values:
m = Δy/Δx = (2 -5)/(-1 -4) = -3/-5 = 3/5 . . . . . . eliminates choices B and C
The slope-intercept equation will then be ...
y = mx + b . . . . . . . generic slope-intercept form
y = 3/5x + b . . . . . . put in m; true for some b that puts the given points on the line
Using the first point, we have ...
5 = 3/5×4 + b
25/5 = 12/5 + b
13/5 = b . . . . . . . . . subtract 12/5
Then the equation is ...
y = 3/5x + 13/5
_____
You know as soon as you consider putting a point value in the equation ...
y = 3/5x + b
that the equation of choice A cannot work. That only leaves choice D.
