If m < 0 and b > 0, the graph of y = mx + b does not pass through which quadrant? Quadrant I
Quadrant II
Quadrant III
Quadrant IV
its Quadrant III
Yes
To determine which quadrant the graph of the equation y = mx + b does not pass through, we need to analyze the given conditions: m < 0 and b > 0.
First, let's understand the equation y = mx + b, where y represents the y-coordinate, x represents the x-coordinate, m is the slope, and b is the y-intercept.
The slope, m, determines the direction of the line. If m > 0, the line slopes upward from left to right, and if m < 0, the line slopes downward from left to right.
In this case, since m < 0, the line will slope downward from left to right.
The y-intercept, b, determines the point at which the line intersects the y-axis. Since b > 0, the line will intercept the y-axis above the origin (where the x-coordinate is 0).
Now, let's consider the quadrants:
Quadrant I is located in the top right portion of the coordinate plane, where both the x and y coordinates are positive.
Quadrant II is located in the top left portion, where the x-coordinate is negative, but the y-coordinate is positive.
Quadrant III is located in the bottom left portion, where both the x and y coordinates are negative.
Quadrant IV is located in the bottom right portion, where the x-coordinate is positive, but the y-coordinate is negative.
Since the line y = mx + b slopes downward (because m < 0) and intersects the y-axis above the origin (because b > 0), it will pass through Quadrants II and III, but it will not pass through Quadrant I and Quadrant IV.
Therefore, the correct answer is Quadrant IV.
sketch somethink like y = 2x + 3 (m>0, b>0 )
and see what you get