The problem involves graphing the equation
and shading the region satisfying the inequalities ,x<3 and y < 2x + 3. The intersection of the shaded regions represents the solution set.
The problem you've provided involves graphing a linear equation and shading a region defined by a set of inequalities on a coordinate grid.
(a) The equation given is y = 2x + 3. This is a linear equation in slope-intercept form, where the slope (m) is 2 and the y-intercept (b) is 3. To graph this equation, we start by plotting the y-intercept at (0,3). Then, we use the slope to find additional points. The slope of 2 means that for every 1 unit increase in x, y increases by 2 units. So, we can plot the points (-2, -1), (-1, 1), (0, 3), (1, 5), (2, 7), (3, 9), and (4, 11) to represent the values of x from -2 to 4. Connecting these points gives us the graph of the equation.
(b) The inequalities given are x < 3, y > 2, and y < 2x + 3. To shade the region that satisfies all three inequalities, we consider each inequality separately. For x < 3, we shade all areas to the left of the vertical line where x equals 3. For y > 2, we shade all areas above the horizontal line where y equals 2. Lastly, for y < 2x +3, we shade all areas below the line of the equation y = 2x + 3. The intersection of these three shaded regions represents the solution set that satisfies all three inequalities simultaneously.