Question 14

The x-intercept of line l is -6.

To find the x-intercept of line l, we first determine the slope of the line using the points (4, 4) and (9, 6). The slope is calculated as (6 - 4) / (9 - 4) = 2/5. Using the point-slope form of a line, we can derive the equation and find that the x-intercept is -6.

A) -6

This option is correct. By calculating the equation of the line using the slope of 2/5 and the point (4, 4), we find that the line can be expressed in the form y = (2/5)x + (6/5). Setting y to 0 to find the x-intercept yields x = -6.

B) -4

This option is incorrect. While -4 is a negative number, it does not satisfy the equation of line l derived from the given points. The calculations indicate that the x-intercept is significantly further left on the x-axis.

C) -2.4

This option is incorrect. The value of -2.4 does not correspond to the x-intercept calculated from the line’s equation. The slope and points yield a much lower x-intercept value.

D) 0.4

This option is incorrect. The x-intercept of 0.4 would imply that the line crosses the x-axis at a positive value, which contradicts the calculated intercept of -6. Thus, this option does not align with the derived equation of the line.

Conclusion

The x-intercept of line l is definitively -6, as confirmed by the calculation of the line's equation and the subsequent evaluation for when y equals zero. All other options fail to represent the correct value derived from the slope and the points provided, demonstrating a clear understanding of linear equations in the xy-plane.