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### Course: Operations and Algebraic Thinking 229+ > Unit 3

Lesson 3: Writing slope-intercept equations- Slope-intercept equation from graph
- Writing slope-intercept equations
- Slope-intercept equation from graph
- Slope-intercept equation from slope & point
- Slope-intercept equation from two points
- Slope-intercept from two points
- Constructing linear equations from context
- Writing linear equations word problems
- Slope-intercept form review

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# Slope-intercept form review

Review slope-intercept form and how to use it to solve problems.

## What is slope-intercept form?

Slope-intercept is a specific form of linear equations in two variables:

When an equation is written in this form, ${m}$ gives the slope of the line and ${b}$ gives its $y$ -intercept.

*Want to learn more about slope-intercept form? Check out this video.*

## Finding slope-intercept equation from features or graph

### Example 1: Equation from slope and intercept

Suppose we want to find the equation of the line whose slope is ${-1}$ and $y$ -intercept is $(0,{5})$ . Well, we simply plug ${m=-1}$ and ${b=5}$ into slope-intercept form!

### Example 2: Equation from two points

Suppose we want to find the line that passes through the points $(0,-4)$ and $(3,-1)$ . First, we notice that $(0,{-4})$ is the $y$ -intercept. Second, we use the two points to find the slope:

Now we can write the equation in slope-intercept:

*Want to try more problems like this? Check out these exercises:*

## Finding features and graph from slope-intercept equation

When we have a linear equation in slope-intercept form, we can quickly find the slope and $y$ -intercept of the corresponding line. This also allows us to graph it.

Consider, for example, the equation $y={2}x{+3}$ . We can quickly tell that the corresponding line has a slope of ${2}$ and its $y$ -intercept is $(0,{3})$ . Now we can graph the line:

*Want to try more problems like this? Check out these exercises:*

## Want to join the conversation?

- How do you an equation into slope intercept from slope and y intercept?(18 votes)
- It's quite easy.

Slope-intercept form: y = mx + b

The "m" is the slope. The "b" is the y-intercept.

So, if the problem tells you the slope = 3/4 and the y-intercept is -5, then you can create the equation by:

-- swap out "m" and put in 3/4

-- swap out "b" and put in -5

You get the equation: y = 3/4 (x) - 5

Hope this helps.(56 votes)

- This has no use in the real world.(8 votes)
- Slope? It can be used later to calculate really important things.(13 votes)

- I still don't know how to graph, this is so hard... :((4 votes)
- y=mx+b

y=y

m=any number

x=x

b=any number

b is the y intercept, which is when x is zero what y is.

Did this help? Or do you not understand how to graph from a slope intercept form?(10 votes)

- how can i graph lines without having the y intercept on the graph?(4 votes)
- You can graph any line from its equation by finding and graphing any 2 points that satisfy the equation.

Alternatively, if you know the slope and any point on the line you can graph the point and use the slope to find more points on the line.

You can find more details in the lessons at this link: https://www.khanacademy.org/math/algebra/two-var-linear-equations(8 votes)

- I don't understand this.(8 votes)
- you said that two years ago i want to see if you will respond to my reply what grade are u in(0 votes)

- how do you find the slope(3 votes)
- Here's my explanation :)

The**slope of the line**is another way of saying**How steep is this line**?

To find an exact number for that, we use the concept**rise over run**.

First, you find two points on the line,*(Let's say our points are (3,3) and (4,5))*

Next you find out how much the line**runs**, aka how much it goes sideways within the two points we picked. To do that, you take the point with the greatest x value, and subtract the x value of the other point:

4-3=1

Now let's find the**rise**aka how much the line goes up within the two points we picked. To do that, we take the y value of our first point, and subtract the y value of our second point:

5-3=2

Now we have our**Rise***(2)*and our**Run***(1)*, so let's put**Rise over Run**:

2/1**simplify**

2

And we have the slope of the line!(5 votes)

- i don't understand how to put x intercept and y intercept in an equation(4 votes)
- You can put the equation into standard from (Ax+By=C) and then convert it into slope-intercept form (y=mx+b). I'm sure there are other ways to attack this problem, but this is how I learned it and it's quite efficient. Hope this helps!(3 votes)

- Does x=my+b count as a slope-intercept form?(5 votes)
- No. You will learn later why when learning functions, but slope-intercept form must always be y=mx+b.(3 votes)

- Does anyone know a good way to solve the linear equations word problems? I don't know how how to find the b in y=mx+b(2 votes)
- The b is the value of the quantity represented by y in the word problem, when the quantity represented by x in the word problem is zero.

For example, if x represents time, then the b can be thought of as the initial (or starting) value of the quantity represented by y.

For example, if y represents the total monthly charge for x kilowatt-hours electricity, and the company charges a constant rate per kilowatt-hour plus a constant monthly service fee, then the b represents the service fee.

Have a blessed, wonderful day!(6 votes)

- I'm having a difficult time determining the polarity of the slope in some of the word problems. For instance, a problem with the Y axis being number of pages left to read in a book, and X being the number of hours reading. I sometimes end up with the signs for the slope flipped because I'm thinking of the total number of pages remaining to be read as a negative value. I'm not sure why I'm doing this. Is there something else I could think about to keep me from flipping these signs?(3 votes)
- The key is to keep the order in which you use your points.

Also, if we had a negative number of pages to read, that would tell us they are already read.

It's like money. If you have $5 to spend, you can go out and bye one gallon of gas due to inflation :).

But if you had -$5, it means you have already spent the money. Just as if you have five pages to read, you will have something to spend 2.5 minutes on. If you have -5 pages to read, you will need to find another book.

I hope this helps!

FreeRadical(4 votes)