what is the graph and linear inquality in two variables 1.4x-3y2x-6 5. y≤½x-3
Answer (1)
Answer:Let's analyze each: 1. 4x - 3y ≥ 2x - 6 - Convert to slope-intercept form (y = mx + b): First, simplify the inequality: 2x - 3y ≥ -6 -3y ≥ -2x - 6 y ≤ (2/3)x + 2 (Remember to flip the inequality sign when dividing by a negative number)- Graphing: 1. Plot the y-intercept: The y-intercept is 2. Plot the point (0, 2).2. Use the slope to find another point: The slope is 2/3. From (0, 2), go up 2 units and right 3 units to find another point (3, 4).3. Draw the line: Draw a solid line through the points (0, 2) and (3, 4). The line is solid because the inequality includes "≤" (less than or equal to).4. Shade the region: Since the inequality is y ≤ (2/3)x + 2, shade the region below the line. This represents all the points (x, y) that satisfy the inequality. 5. y ≤ (1/2)x - 3 - Graphing: 1. Plot the y-intercept: The y-intercept is -3. Plot the point (0, -3).2. Use the slope to find another point: The slope is 1/2. From (0, -3), go up 1 unit and right 2 units to find another point (2, -2).3. Draw the line: Draw a solid line through the points (0, -3) and (2, -2). The line is solid because the inequality includes "≤" (less than or equal to).4. Shade the region: Since the inequality is y ≤ (1/2)x - 3, shade the region below the line. This represents all the points (x, y) that satisfy the inequality. In summary: Both inequalities are linear inequalities in two variables. They are graphed as lines (solid lines because of "≤"), and the region satisfying the inequality is shaded below the line in both cases. The difference lies in their slopes and y-intercepts, resulting in different lines and shaded regions on the coordinate plane.
