I'm having a very hard time with graphing and I can't seem to figure out how to graph inequalities. I appreciate any help that you have to offer me.
x + y < 1
let's solve for y
=> y < -x + 1
hmm, if not for the inequality sign,this would look like a line, with slope -1 and y intercept 1, and that's what we will draw. however, since it is an inequality, we have to shade the region where y is less than the values given by the line. the line is not included in the solution since we have a strictly less than sign, so we must draw a broken line. see below
y <= 2x + 1
well, this isn't exactly the same story, since we don't have to simplify anything, they gave us in the useable form.
what does this remind you of?...i hope it reminds you of a line with slope 2 and y-intercept + 1, we will graph that line and shade the region under it, since we want y less than or equal to the value of the line. since we can be equal to the values of the line, the line we draw is solid and is included in the solution
just kidding, i'm kind of bored at the moment anyway, besides, this is a bit different from the other problems.
we have 2 inequalities, and we will graph both at the same time
y > x + 1
y < (3/2)x + 3
so, these are in the nice form again. let's graph these lines.
now here i drew the lines bright and bold, howerever, both should be broken, i had to do it like that so you could see them. the grey region satisfies the first inequality, the blue region satisfies the second, the pink region satisfies both simultaneously, and the unshaded region satisfies neighter. i hope you understand the graph and why the regions are shaded the way they are. if you are unclear about it, say so