Question

A line with a negative slope and a negative

y-intercept is graphed on a coordinate
plane. Which quadrant will the line not pass
through? Justify your response.

Answer 1

A line with a negative slope and a negative y-intercept will not pass through Quadrant I.

A line with a negative slope indicates that as the x-value increases, the y-value decreases. A negative y-intercept means that the line intersects the y-axis below the origin.

Quadrant I is the region of the coordinate plane where both x and y are positive. Since the line has a negative slope and a negative y-intercept, it will not intersect Quadrant I.

As the x-value increases in Quadrant I, both x and y will be positive, which contradicts the line's negative slope. Additionally, the line's negative y-intercept places it below the x-axis, further preventing it from intersecting Quadrant I.

Therefore, the line will pass through Quadrants II, III, and IV, but not Quadrant I.

Answer 2

First quadrant will the line not pass.

Explanation:

The given line has a negative slope. It means with increasing value of x, y will be decreasing. It has a negative y-intercept that is at x = 0, y is less than 0.

If the value of x will be greater than 0, the value of y will be going downwards continuously.

If x > 0, y < 0, as the line has a negative y-intercept.

A point in first quadrant means x > 0 as well as y > 0.

Hence, the line cannot pass through the first quadrant.