In order to graph an equation, you must first plot the y intercept (the “b” in y=mx+b), and go from there. I’ll help you with a few! :)
1) take a look at the y intercept -3. Start at the origin, (0,0) aka the middle of the graph. Plot a point three units down, (0,-3). Now, take the slope, 2/1. Think of the slope as rise/run, so make your second point at (1,-1) (2 up, 1 to the right from your y intercept). Draw a line through the two points, (0,-3) and (1,-1).
5) for this one, we have to solve for y. Subtract x from both sides of the equation to get y=-x+4. Let’s plot the y intercept like last time, at (0,4). Since the slope -1/1 is negative, we will go down 1, and 1 to the right from (0,4). Draw a line through the two points.
6) this problem does not have a slope. It only has a y intercept of 3. Since it does not have a slope, the line is flat. So, draw a straight, horizontal line through (0,3). This means that x has infinitely many solutions, but y will always be 3.
Extra tip: My old math teacher was a volleyball coach. Here’s something she shared with us to remember how to graph negative versus positive slopes. At practice, we’d walk up and down a hill to work our muscles. On the way up, we’re working our muscles, strengthening our bodies, so it’s considered positive. From left to right, the slope of the hill goes up and it is positive. On the way down, your muscles are resting, and the girls are most likely gossiping, so it is considered negative. From left to right, the slope goes down, and it is negative.
Here are 2 bowls. One of them has 25 gems and the other has 15 gems. Some of them are red. All the gems from the two bowls are now put into a third bowl. What fraction of the gems in the third bowl will be red?
