Question

How do you graph the inequality `4x+6y>=10`?

Answer 1

Refer to the explanation.

Explanation:

`4x+6y>=10` is in the standard form for a linear equation. Solve for `y` to convert to the slope-intercept form, `y=mx+b`, where `m` is the slope and `b` is the y-intercept.

`4x+6y>=10`

Subtract `4x` from both sides.

`6y>=10-4x`

Divide both sides by `6`.

`y>=10/6-4/6x`

Simplify.

`y>=5/3-2/3x`

Rearrange.

`y>=-2/3x+5/3`

Determine 2 points on the line. Then plot the points and draw a straight solid line through the points to indicate that the line is part of the graph. Then shade the graph above the line.

`x=0,` `y=5/3`

`x=2,` `y=1/3`

graph{y>=-2/3x+5/3 [-10, 10, -5, 5]}