HA1-398 Check out these examples to help you learn more about slope, equations, and identifying graphs of linear equations.

Problem type 1: I have a point and the slope, what’s the line look like? Even though we will quickly know the answer to this problem, we will use it to explain the steps you can take to find the correct line. The Steps are Is it a positive or negative slope? Knock out answers that don’t fit. Plot my given point, if my point IS NOT on the line, it’s not the answer. Use my slope (RISE/RUN) as a MAP to my next point on the line.

Example 1: I have a point and the slope, what’s the line look like? STEP 1:First, Look to see if you are given a positive or negative slope. Remember this about positive and negative slope. Negative Slope Positive Slope WEE….this downhill is easy, don’t be so negative. I’m positive this uphill is hard work Positive Slope Negative Slope

Example 1: I have a point and the slope, what’s the line look like? So since I am looking for a positive slope of 2, I know A Can’t be my answer because it Is a negative slope line. STEP 2: Plot the given point, ( 3,1), in this example, and see if it is on our line. If (3,1) is NOT on our line, then that line CANNOT be the answer. Negative Slope

Example 1: I have a point and the slope, what’s the line look like? Step 2: plot (3,1). Both lines have the point (3,1), so this does not help us find our answer. Step 3: Use Slope. Our slope is 2 in this example. Use slope of 2 to see which line fits a RISE/RUN of 2/1.

Example 1: I have a point and the slope, what’s the line look like? For A: If we start at (3,1) and RISE 2 and then RUN 1, we are NOT on our line, so this CAN’T be our answer. For B: If we start at (3,1) and RISE 2 and then RUN 1, we ARE on our line, so this IS our answer. Step 3: Use Slope, 2 in this example, to see which line fits a RISE/RUN of 2/1.

Example 1: I have a point and the slope, what’s the line look like? In summary, our steps were - STEP 1: Do we have a positive Or negative slope. Knock out wrong answers - STEP 2: Plot the given point, knock out lines that don't have that point. STEP 3: Use RISE/RUN of the given slope as a map to another point on the line. Knock out answers that don’t bring you back to your line. Use these strategies on the next problem. Make sure you try to ID the correct line before you click for the answer.

Try it before you CLICK for answer. Practice Problem #1 Try it before you CLICK for answer. 3 Steps positive or negative slope line? Plot my given point. Use given slope, and RISE/RUN from my given point, to see if I end back on the line.

Practice Problem #1 Positive Slope Negative Slope Positive Slope STEP 1: Positive or Negative slope? 2 is a positive slope, so choice A CANNOT be our answer. Positive Slope Negative Slope Positive Slope Positive Slope

Practice Problem #1 Positive Slope Negative Slope Positive Slope STEP 2: Plot our point. Our point is (-5, -6). Let’s see which choices have the point on the line. Only this graph has (-5, -6) on it, and would seem to be our answer. Positive Slope Negative Slope Positive Slope Positive Slope Let’s confirm this by looking at our RISE/RUN of 2/1 on choice B.

Practice problem #1 Let’s confirm this by looking at our RISE/RUN of 2/1 on choice B. We can see that when we RISE 2 and RUN 1 from point (-5, -6), we land back on the line, meaning this IS our answer.

Problem type 2: I have slope intercept equation and I need to identify the graph. Let’s review Slope intercept form , y=mx+b, before we tackle this next problem.

Slope Intercept Form Review, y=mx+b If we have a y=mx + b equation of y = -2x + 4 , how can it help us graph? Let’s break it down! y= mx + b y = -2x + 4 The m stands for the slope of the line, and you know from a previous lesson that slope = RISE over RUN In this example, our slope is -2. In RISE/RUN it looks like this. We always put whole #’s over 1. m = rise run m = -2 1 This RISE/RUN slope will help us graph our line in a second.

Slope Intercept Form review, y=mx+b We know our y=mx + b equation is y = -2x + 4 , how can it help us graph? Let’s break it down! y= mx + b y = -2x + 4 Let’s LEARN! The b stands for the y intercept, where our line CROSSES or intersects with the y-axis. Having this info gives a starting point for our line. In this example, our y intercept is at 4 on the y=axis, or the point ( 0,4) Now we have a slope of -2/1 , and a y intercept point of ( 0,4), we can graph this line.

Slope Intercept Form review, y=mx+b Equation: y = -2x + 4 , Slope is -2/1 , y-int.: 4 We start by putting a point at 4 on the y-axis, our y intercept. THEN, we use our slope as a roadmap to the next point. -2/1 means DOWN 2, to the RIGHT 1 y x This is our next point, and we ONLY need two points to make a line. DRAW the line. NOTE: An equation like y = 2x is in slope intercept form. If the “b” is missing, it is a 0. It would look like this if we wrote it out. Y=2x + 0 with a slope of 2 and a y intercept of 0. Y= -1/2x is really y= -1/2x +0 , a line with a slope of -1/2 and a y int. of 0.

Let’s tackle this next problem using our slope intercept knowledge. Problem type 2: I have slope intercept equation and I need to identify the graph. Let’s tackle this next problem using our slope intercept knowledge. This could be it Wrong y int. Step 1: Pick out slope and y intercept in equation. Slope: 2, y int: -4 Step 2: Knock out choices of lines that don’t match our positive slope. Step 3: Knock out choices of lines that don’t have y intercept of -4. Wrong y int. Negative Slope

Let’s tackle this next problem using our slope intercept knowledge. Problem type 2: I have slope intercept equation and I need to identify the graph. Let’s tackle this next problem using our slope intercept knowledge. Wrong y int. Step 4: Use RISE/RUN to confirm our choice. YES!! When we RISE 2 and RUN 1, we land back on the line. This is it!! Wrong y int. Negative Slope

Try it before you CLICK for answer. 4 Steps ID slope and y-int. from equation positive or negative slope line? Check y-intercept Use given slope, and RISE/RUN from my y int. to see if I end back on the line. Problem type 2: I have slope intercept equation and I need to identify the graph. You try this one before you click for answer.

You try this one before you click for answer. Problem type 2: I have slope intercept equation and I need to identify the graph. You try this one before you click for answer. Step 1: Pick out slope and y intercept in equation. Slope: -2/3, y int: 1 Step 2: Knock out choices of lines that don’t match our negative slope. Positive Slope Step 3: Knock out choices of lines that don’t have y intercept of +1. Doesn’t help in this problem, they both y int. of +1. On to RISE/RUN Positive Slope

We’re down to choice A or B, and need to use RISE/RUN to decide. Problem type 2: I have slope intercept equation and I need to identify the graph. This one is close, but you can see our RUN goes beyond the line. NOT the answer! We’re down to choice A or B, and need to use RISE/RUN to decide. Step 4: Step 4: Use RISE/RUN to confirm our choice. Our slope is -2/3, let’s see which one works. This one is perfect! DOWN 2 and RIGHT 3 lands right on the line. This IS our answer! Positive Slope Positive Slope

Word Problem graphs Positive Slope Positive Slope A goes down from 11,500 to 10,000 in one year. That is $1500 per year, not $2000/year. This CANNOT be our answer. B goes down from 11,500 to 9,500 in one year. That is $2000/year. This IS our answer. Couple of tips here. The value of the item. Or starting point is always your y intercept. Here it is $11,500, and all the graphs are on $11,500 on the y axis, so it isn’t very helpful in this problem. So we need to use our SLOPE knowledge. We are looking at a motorcycle “depreciating” in value, that is going DOWN, a negative slope. C and D are positive slopes and CANNOT be the answer. Positive Slope Positive Slope We have to use RISE/RUN to figure this out. -2000 per year is a slope of -2000/1, so our graph needs to go down $2000 for every year.

Try it before you CLICK for answer. Steps positive or negative slope line? Check y-intercept, the beginning value Use given slope, and RISE/RUN from y int. to see if I end back on the line. Word Problem graphs

Word Problem graphs A goes up, and it looks like $50 in one year, and $100 in 2 years, which fits our slope. This is our answer. Couple of tips here. The value of the item. Or starting point is always your y intercept. Here it is $500, and all the graphs are there, so it isn’t very helpful in this problem. So we need to use our SLOPE knowledge. We are looking at a stock increasing in value, that is going UP, a positive slope. B is a negative slope and CANNOT be the answer. D goes up, but $50 in 4 years. That doesn’t work. C goes up, but $75 in 8 years. That doesn’t work. We have to use RISE/RUN to figure this out. +50 per year is a slope of 50/1, so our graph needs to go up $50 for every year.