Answer:
See graph, but the points you need are (0,3) and (3,0)
Explanation:
I've attached a picture of what the graph looks like, so take a look at that first.
Here's how you manually plot an equation like that: simply pick a value for x, plug it into the equation, and see what comes out. That's y. Put them together and plot the point.
It's easiest to start with x=0. So solving the equation for x=0, we get:
y = -0 + 3 = 3 Do you see that point on my graph? It's (0,3).
Now let x=1:
y = -1 + 3 = 2 That point is on my graph too.
Keep going like that if you want. I did enough points to get just past both axes, because that's sometimes useful.
So I've graphed the equation, but I didn't use the "slope-intercept method" they specified. Okay, no problem.
What does intercept mean? It means the Y-axis intercept, the place where the graph crosses the y-axis.
Looking at my graph you can tell that's at y=3.
But they want you to recognize that the 3 in the equations is the intercept term. It's what y is when x is 0. We did that above and found out that y is 3 then, so the intercept is the point (0,3).
Cool, we have the intercept, and if you hadn't graphed it already, that's the only point you'd have on your graph paper.
But they want us to use the "slope" too. Where is the slope term in that equation? It's the coefficient in front of x, the -1. (It's normally not shown, but there's a 1 there.) But the important thing to notice is the negative sign: that means the line goes down and to the right.
And slope is also "rise" over "run", or how much y changes as x changes.
But if the slope is 1, then y changes at the same rate as x. And since this one is negative, as x gets bigger, y gets smaller.
Now, you could use this idea and move x right 3 units, which would mean y had to go down by 3 units, so you'd end up at (3,0). That would be a 2nd point and you could draw the line.
But what I THINK they mean by "slope intercept method" is to ALSO find out where the graph crosses the x-axis. Because remember, the 3 term told us what y was when x was 0.
But now let's let y=0 and compute what x is:
0 = -x + 3 --> x=3
And boom, we're back at (3,0), which is where that function crosses the x-axis.