Graph of solution of linear inequality 3x-4y>2?

Question

I worked it as follows:
3x-4y>2
=3x-3x-4y>-3x+2
=y<3/4-2/4
=y<3/4-1/2
I know my line is dashed, but I'm not sure my solution is correct and I'm unsure of the line's location.

Answer 1

It looks like you solved the inequality correctly. The line would have a y-intercept at 1/2 (halfway between the origin and 1 on the y-axis). Since the slope is 3/4, from there you'd count up 3 and over 4 to find another point-----which would be the point (4,3.5). You are correct that the line is dotted. Since the final equation says y is LESS THAN the line, you'd shade BELOW that dotted line.

Answer 2

Your solution is correct, although you dropped the x ... I assume you mean y < 3/4x - 1/2

Think about the standard formula for a line: y = mx + b where m is the slope and b is the x-intercept. You need to graph a line with a slope of +3/4 and x-intercept of -1/2. If that doesn't ring a bell, review your notes/book on graphing lines in the coordinate plane.

If you can't figure out whether to shade the graph above or below the line, pick a point on one side and plug it into the equation. If the statement is true, that is, the y-value of the point is less than 3/4 times the x-value minus 0.5, that's the side you shade. If OTOH the point you chose gives you a false statement (the y value is larger), shade the other side of the line.