Question 6

y=31x−1

This equation represents the line graphed above, demonstrating that it has a positive slope and crosses the y-axis at -1.

A) y=−31x+1

This option indicates a line with a negative slope of -31, which does not match the slope of the line in the graph. Additionally, the y-intercept of +1 is also inconsistent with the graph, confirming that this is not the correct equation.

B) y=31x−1

This option correctly shows a positive slope of 31, indicating a steep incline, and has a y-intercept of -1, which aligns perfectly with the graph depicted. Therefore, this option accurately represents the line.

C) y=3x-1

While this equation has the correct y-intercept of -1, its slope of 3 is not steep enough to match the slope of the graphed line, which is much steeper. Thus, this option fails to represent the line accurately.

D) y=-3x-9

This option indicates a negative slope of -3 and a y-intercept of -9. Both the slope and the y-intercept differ significantly from those of the graphed line, making this option incorrect.

Conclusion

The correct equation of the line is y=31x−1, as it accurately reflects both the slope and y-intercept observed in the graph. The other options fail to match either the slope or the y-intercept, confirming their incorrectness when compared to the graphed line.