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The graphed line shown below is y = 5 x minus 10.

On a coordinate plane, a line goes through (2, 0) and (3, 5).

Which equation, when graphed with the given equation, will form a system that has no solution?
A. = negative 5 x + 10
B. y = 5 (x + 2)
C. y = 5 (x minus 2)
D. y = negative 5 x minus 10

1 answer

To form a system that has no solution, the two equations must represent parallel lines, which means they have the same slope but different y-intercepts.

The given equation is: \[ y = 5x - 10 \]

The slope of this line is 5. Now, let's analyze the options:

A. \( y = -5x + 10 \)

  • Slope = -5 (Different slope, so this is not parallel)

B. \( y = 5(x + 2) = 5x + 10 \)

  • Slope = 5 (Same slope, but different y-intercept, so this is parallel)

C. \( y = 5(x - 2) = 5x - 10 \)

  • Slope = 5 (Same slope and same y-intercept, so this is the same line)

D. \( y = -5x - 10 \)

  • Slope = -5 (Different slope, so this is not parallel)

The only equation that has the same slope (5) but a different y-intercept is option B. Therefore, when graphed with the given equation, \( y = 5(x + 2) \) will form a system that has no solution.

The correct answer is: B. \( y = 5(x + 2) \).