#Linear Inequality

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Graphing a linear inequality is a way to show all of the solutions on the coordinate plane. When an inequality is written in slope-intercept form (like y ≥ −⅓x + 1), you can use the slope and y-intercept to draw the boundary line and then shade the correct side. For example, with the inequality: y ≥ −⅓x + 1 Step 1: Identify the slope and y-intercept. Compare to y = mx + b. Here, the slope is m = −⅓ and the y-intercept is b = 1. Step 2: Plot the y-intercept. Start at (0, 1) on the y-axis and put a point there. Step 3: Use the slope to find another point. Slope −⅓ means “down 1, right 3.” From (0, 1), move down 1 and right 3 to get (3, 0). Plot that point. You can repeat this pattern to get more points on the line. Step 4: Draw the boundary line. Connect the points with a straight line. Because the inequality is ≥ (greater than or equal to), draw a solid line to show that points on the line are included. Step 5: Decide which side to shade (no test point). The inequality says y is greater than or equal to the line. That means every solution has a y-value that is above the line. Shade the entire region above and including the line. Solution: Every point in the shaded region (including the solid line) makes the inequality y ≥ −⅓x + 1 true. “For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life.” - John 3:16 #alldayeverydaymath #math #algebra #algebra1 #algebrahelp #fyp

Linear Ordinary Differential Equation

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