the problem is:
3x-4y<12
so i came up with this:
after solving for y=mx+b
y< (3)/(4)x-3
and two points that i got for the graph was:
(0,-3)and(4,0)
and when i graph the line is dashed and the solution is going on bottom of
the line
It seems like you are encountering a problem with solving and graphing the inequality 3x - 4y < 12. Let me break it down for you step by step.
1. Start with the given inequality: 3x - 4y < 12.
2. Solve for y by isolating it on one side of the inequality. To do this, subtract 3x from both sides: -4y < -3x + 12.
3. To get y alone, divide both sides by -4. Remember, when you divide or multiply both sides of an inequality by a negative number, the inequality sign flips: y > (3/4)x - 3.
4. Your expression y > (3/4)x - 3 represents the inequality in slope-intercept form (y = mx + b), where m is the slope (3/4) and b is the y-intercept (-3).
5. Now, let's plot the graph. Since the inequality is y > (3/4)x - 3, the line will be dashed because y is not equal to (3/4)x - 3. It's only greater than.
6. Start by plotting the y-intercept, which is -3. Mark the point (0, -3) on the graph.
7. Determine a second point on the line. Plug in x = 4 into the equation y = (3/4)x - 3 and solve to find y. When x = 4, y = (3/4)(4) - 3 = 0. Mark the point (4, 0) on the graph.
8. Draw a dashed line passing through the two plotted points. Make sure the line is slanted upwards to represent the positive slope (3/4).
9. Finally, since the inequality is y < (3/4)x - 3, the solution area will be below the dashed line. Shade the region below the line to represent the solutions to the inequality.
If you have any further questions or need clarification on any step, feel free to ask!