can u graph the inequality in a coordinate plane
1)y>3x-1
2)-x>2
Certainly! To graph an inequality on a coordinate plane, we need to follow a few steps.
1) Graphing y > 3x - 1:
a) First, graph the line y = 3x - 1 as if it were an equation. This is a straight line with a y-intercept of -1 and a slope of 3 (rise 3/run 1).
b) Since we have a "greater than" inequality, we need to determine whether the region above or below the line should be shaded. To do this, choose a test point not on the line.
c) Let's choose the origin (0, 0) as the test point. Substitute the x and y coordinates of the test point into the inequality (y > 3x - 1).
- Since 0 is greater than -1, the inequality is true, and the region above the line is shaded.
d) Finally, draw a dashed line to represent y = 3x - 1 since the symbol ">" does not include equality. Shade the region above the line to indicate the solution set.
2) Graphing -x > 2:
a) Start by isolating x. Multiply both sides of the inequality by -1, and remember to reverse the inequality symbol since we are multiplying by a negative number (-1).
- (-x) becomes x, and the inequality becomes x < -2.
b) Graph the line x = -2 as if it were an equation. This is a vertical line passing through -2 on the x-axis.
c) Since we have a "less than" inequality, we need to determine whether the region to the left or right of the line should be shaded. To do this, choose a test point not on the line.
d) Let's choose the origin (0, 0) as the test point. Substitute the x and y coordinates of the test point into the inequality (x < -2).
- Since 0 is less than -2, the inequality is true, and the region to the left of the line is shaded.
e) Finally, draw a dashed line to represent x = -2 since the symbol "<" does not include equality. Shade the region to the left of the line to indicate the solution set.
By following these steps, you can graph the given inequalities in a coordinate plane.