how do figure out how to graph y>1/5x-2
5y-x<10?
To graph the inequalities y > 1/5x - 2 and 5y - x < 10, you can follow these steps:
1. Start by rewriting both inequalities in slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
For the inequality y > 1/5x - 2:
- Add 2 to both sides: y + 2 > 1/5x
- Rewrite: y > 1/5x + 2
For the inequality 5y - x < 10:
- Add x to both sides: 5y < x + 10
- Divide all terms by 5: y < 1/5x + 2
2. Now that both inequalities are in slope-intercept form, you can easily identify the slope and y-intercept of each equation:
For y > 1/5x + 2:
- The slope is 1/5, meaning for every increase in x by 1, y increases by 1/5.
- The y-intercept is 2, meaning the line crosses the y-axis at (0, 2).
For y < 1/5x + 2:
- The slope is 1/5, just like the previous equation.
- The y-intercept is also 2.
3. Graph each inequality separately:
For y > 1/5x + 2:
- Draw a dashed line with a slope of 1/5 passing through the y-intercept at (0, 2).
- Since it is "greater than" (not "greater than or equal to"), make the line dashed.
- Shade the area above the line because y is greater than the expression.
For y < 1/5x + 2:
- Draw a dashed line with a slope of 1/5 passing through the y-intercept at (0, 2).
- Shade the area below the line because y is less than the expression.
Keep in mind that in both cases, the lines are dashed to indicate that they do not include the points on the line itself.
4. The solution to this system of inequalities is the region where the shaded areas overlap. This indicates the values of x and y that satisfy both inequalities.