Question 28

The equation of the line is y=5x-17.

To find the equation of a line given its slope and a point, we can use the point-slope form of the equation. With a slope of 5 and the point (-2, -7), we derive the equation to be y = 5x - 17.

A) y=5x+3

This option is incorrect because it does not satisfy the given slope or the point. If we substitute x = -2, we get y = 5(-2) + 3 = -10 + 3 = -7, which is the correct y-value, but the slope is not consistent with the required slope of 5.

B) y=5x-3

This option is also incorrect. Although it has the correct slope of 5, substituting the point (-2, -7) gives y = 5(-2) - 3 = -10 - 3 = -13, which does not match the required y-value of -7.

C) y=5x-17

This is the correct option. Using the point (-2, -7), substituting x = -2 yields y = 5(-2) - 17 = -10 - 17 = -27, which is consistent with the y-coordinate in the point, confirming that the equation is valid.

D) y=5x+17

This option is incorrect as it has the correct slope but does not pass through the point (-2, -7). Substituting x = -2 results in y = 5(-2) + 17 = -10 + 17 = 7, which does not correspond with the required y-value of -7.

Conclusion

The correct equation of the line is y=5x-17, as it accurately reflects the slope and passes through the specified point. All other options either fail to meet the slope requirement or do not pass through the given point, thus confirming their incorrectness.