HELP I DONT GET THIS
10. 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 .
We can't draw graphs on this forum. I will try to copy one. If it turns out well you can see which quadrant is empty.
http://www.math.com/school/subject2/lessons/S2U4L2DP.html
Thank you DrBob222!
Let's illustrate with an example that fits your description
y = -3x - 4
https://www.wolframalpha.com/input/?i=plot+y+%3D+-3x+-+4
Note that the graph could not possible pass through quad I
Note that the graph I showed has a positive slope. It does have a negative y intercept but barely.
To determine which quadrant the line will not pass through, we need to understand the characteristics of a line with a negative slope and a negative y-intercept.
1. Negative Slope: A negative slope means that the line slopes downward from left to right. It indicates that as the x-values increase, the y-values decrease.
2. Negative y-intercept: The y-intercept is the value where the line intersects the y-axis. When the y-intercept is negative, it means that the line crosses the y-axis below the origin (0,0).
To justify our response, we need to consider the four quadrants on a coordinate plane:
1. Quadrant I: This quadrant is located in the top right of the coordinate plane. In this quadrant, both the x-values and y-values are positive. Here, the line will pass through because it has a negative slope and starts below the origin.
2. Quadrant II: This quadrant is located in the top left of the coordinate plane. In this quadrant, the x-values are negative, but the y-values are positive. Here, the line will pass through because it has a negative slope.
3. Quadrant III: This quadrant is located in the bottom left of the coordinate plane. In this quadrant, both the x-values and y-values are negative. Here, the line will not pass through because it has a negative y-intercept, which places it below the origin.
4. Quadrant IV: This quadrant is located in the bottom right of the coordinate plane. In this quadrant, the x-values are positive, but the y-values are negative. Here, the line will pass through because it has a negative slope.
Based on the characteristics of the line with a negative slope and a negative y-intercept, it will not pass through Quadrant III, which is the bottom-left quadrant.