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### Course: 8th grade (Eureka Math/EngageNY) > Unit 4

Lesson 3: Topic C: Slope and equations of lines- x-intercept of a line
- Intercepts from a table
- Intercepts from a graph
- Intercepts from an equation
- Worked example: intercepts from an equation
- Intercepts from an equation
- Slope & direction of a line
- Intro to slope
- Slope formula
- Worked example: slope from graph
- Slope of a line: negative slope
- Slope from graph
- Worked example: slope from two points
- Slope of a horizontal line
- Slope from two points
- Intro to slope-intercept form
- Slope-intercept intro
- Slope from equation
- Graph from slope-intercept equation
- Graph from slope-intercept form
- Slope-intercept equation from graph
- Slope-intercept equation from graph
- Slope-intercept equation from slope & point
- Slope-intercept equation from two points
- Slope-intercept from two points
- Slope-intercept form from a table
- Converting to slope-intercept form
- Slope-intercept form problems
- Proving slope is constant using similarity
- Intro to point-slope form

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# Intro to slope

Walk through a graphical explanation of how to find the slope from two points and what it means.

We can draw a line through any two points on the coordinate plane.

Let's take the points $(3,2)$ and $(5,8)$ as an example:

The slope of a line describes how steep a line is. Slope is the change in $y$ values divided by the change in $x$ values.

Let's find the slope of the line that goes through the points $(3,2)$ and $(5,8)$ :

Notice that both of the lines we've looked at so far have been increasing and have had positive slopes as a result. Now let's find the slope of a decreasing line.

## Negative slope

Let's find the slope of the line that goes through the points $(2,7)$ and $(5,1)$ .

Wait a minute! Did you catch that? The change in $y$ values is negative because we went from $7$ down to $1$ . This led to a negative slope, which makes sense because the line is decreasing.

## Slope as "rise over run"

A lot of people remember slope as "rise over run" because slope is the "rise" (change in $y$ ) divided by the "run" (change in $x$ ).

## Let's practice!

*Heads up! All of the examples we've seen so far have been points in the first quadrant, but that won't always be the case in the practice problems.*

## Challenge problems

See how well you understand slope by trying a couple of true/false problems.

## Want to join the conversation?

- why does math have to be so confusing?(64 votes)
- If you work hard then eventually math won't be as confusing!(19 votes)

- My dad left to get milk. He never came back :)(46 votes)
- My mom gets milk every week, and she always comes back! I confuse.(7 votes)

- How can the slope value (1/2 or 5) be used in real life, and how can we use it in math?

Thanks!(37 votes)- It could be used to simulate the steepness of a mountain/hill.(18 votes)

- Genuine question- when will i EVER use this IRL?(19 votes)
- no but you will for your math class so(22 votes)

- Can somebody tell me how to easily visualized. which slope is steeper?(8 votes)
- Try to think about it like this, imagine you are running up (positive slope) or down (negative slope) a flight of stairs.

If the slope is a larger number, than it is the same as taking several steps at once.

If the slope is a smaller number, it is as if you are taking less steps at once, not going up the flight of stairs as quickly.

Imagine a slope of 1, means for ever step you take with your feet you only go up one stair.

Imagine a slope of 5, this means for every step you take you go up 5 stairs. You get to the top and rise much quicker.*___________*

Another visual example: Imagine you are going skiing. As you go down a slope, you expect the slope to be negative. You come from up high on the y axis and go down.

If now you go to a ski slope at -5 that means for every meter you glide forward on your skis towards to bottom of the hill (x-axis), you also go down 5 meters on the hills height (y-axis). This is very steep as you can imagine.

Now imagine you are going down a ski slope of only 1/2. This means for every 1 meter you glide forward on your ski you only get 1/2 meter further down the hills height.(32 votes)

- ma’am I do not get this🧍🏻♀️(21 votes)
- who are you talking to(1 vote)

- lmao what is y=mx+b gonna do for me in life(17 votes)
- basically unless you plan to be a nerd you wont need it(1 vote)

- So it doesn't matter then, what numbers you use for slope. What about when they don't give you a graph and make you find slope? I'm confused(8 votes)
- You haven't said what information you were given instead of a graph.

If you are given two points on the line, you can calculate the slope using the slope formula.

If you are given the equation of the line, you can:

-- Change the equation into slope-intercept form: y=mx+b and "m" will be the slope.

-- Or, you can calculate two points using the equation and then use the slope formula to calculate the slope.

All these options are covered in later videos.(5 votes)

- Is there another way of finding a slope without a graph?(4 votes)
- It should give you points on the graph, use the formula y2-y1/x2-x1, to find the slope, (y2 a y-coordinate, of one of the point, you are not multiplying anything)

Hope this helps :)(12 votes)

- how does this affect me(9 votes)
- You can use it to program. And to calculate landslides the steepness of hills or the angle of a roof.(1 vote)