Question

Graph the linear inequality
y<-2x+3

Answer 1

graph the line -2x+3 as a dotted line and shade in below that line.

Explanation:

Linear Inequalities:

Linear inequalities are an inequality... which contain linear equations. To graph these linear inequalities it helps to first just graph the linear equation and then based on the inequality whether it's less than, less than or equal to, greater than, or greater than or equal to we would draw above or below this line and with a solid or dotted line.

So we're given the equation:
`y < -2x+3` it helps to first just graph the -2x + 3, which we can do by starting at the y-intercept of 3 and then going down 2 and going right 1 as defined by the slope -2. Likewise we can go up 2 and go left 1 from the y-intercept to define points to the left of the y-axis.

Now from here we look at the inequality:
`y < -2x+3`, it's telling us y values less than -2x + 3, so we want to be below the line we just graphed, so shade below the line. One thing to note is it's a less than and not a less than or equal to so the line it self is not included, meaning we draw a dotted line.

I included a desmos graph which further illustrates how this would look.