Answer:
he point (-1, 0) is a valid solution, and the inequality is correctly written
Explanation:
There are three standard forms for linear inequalities:
Standard form: Ax + By > C
Slope-intercept form: y > mx + b
Point-slope form: y - y1 > m(x - x1)
To write an inequality in standard form, you need to know the coefficients of the variables (A and B) and the constant term (C). You can find these values by examining the slope and the y-intercept of the line representing the inequality. For example, suppose the graph of the inequality shows the solution set to be all the points that lie above the line y = 2x + 1. To write this inequality in standard form, we can set A = 2, B = 1, and C = 1. The resulting inequality is 2x + y > 1. To check our work, we can substitute a test point, such as (-1, 0), into the inequality to see if it is a valid solution. In this case, we have 2(-1) + 0 > 1, which simplifies to -2 > 1, which is not true. Therefore, the point (-1, 0) is not a valid solution, and the inequality is correctly written.
To write an inequality in slope-intercept form, you need to know the slope (m) and the y-intercept (b) of the line representing the inequality. For example, suppose the graph of the inequality shows the solution set to be all the points that lie above the line y = 2x + 1. To write this inequality in slope-intercept form, we can set m = 2 and b = 1. The resulting inequality is y > 2x + 1. To check our work, we can substitute a test point, such as (-1, 0), into the inequality to see if it is a valid solution. In this case, we have 0 > 2(-1) + 1, which simplifies to 0 > -2 + 1, which is true. Therefore, the point (-1, 0) is a valid solution, and the inequality is correctly written.
To write an inequality in point-slope form, you need to know the slope (m) and a point (x1, y1) on the line representing the inequality. For example, suppose the graph of the inequality shows the solution set to be all the points that lie above the line y = 2x + 1. To write this inequality in point-slope form, we can choose a point on the line, such as (0, 1), and set x1 = 0 and y1 = 1. The slope of the line is m = 2, so the resulting inequality is y - 1 > 2(x - 0). This simplifies to y > 2x + 1, which is the same as the inequality written in slope-intercept form. To check our work, we can substitute a test point, such as (-1, 0), into the inequality to see if it is a valid solution. In this case, we have 0 > 2(-1) + 1, which simplifies to 0 > -2 + 1, which is true. Therefore, the point (-1, 0) is a valid solution, and the inequality is correctly written.