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### Course: Algebra 1 > Unit 5

Lesson 6: Summary: Forms of two-variable linear equations# Forms of linear equations: FAQ

Frequently asked questions about forms of linear equations

## Where are linear equations used in the real world?

There are countless applications for linear equations in the real world! For example, engineers might use linear equations to study the relationships between different physical properties, like force and displacement. Economists might use linear equations to model supply and demand, or to predict future trends.

Practice with our Linear equations word problems
exercise.

## What is slope-intercept form?

Slope-intercept form is one way to write a linear equation. The form is $y=mx+b$ , where $m$ is the slope of the line and $b$ is the $y$ -intercept.

Practice with our Slope-intercept intro
exercise.

## How can we graph a slope-intercept equation?

Start by finding the $y$ -intercept, or the point where the line crosses the $y$ -axis. Plot that point first. Then, use the slope to find other points on the line. Remember that slope is "rise over run" - if the slope is positive, the line will go up as it goes to the right, and if the slope is negative, the line will go down as it goes to the right.

Practice with our Graph from slope-intercept form
exercise.

## How can we write an equation in slope-intercept form?

We need two pieces of information: the slope and the $y$ -intercept. Once we have those, we substitute the values in for $m$ and $b$ in the equation $y=mx+b$ .

Practice with our Slope-intercept equation from graph
exercise.

## What is point-slope form?

Point-slope form is another way to write a linear equation. The form is $y-{y}_{1}=m(x-{x}_{1})$ , where $m$ is the slope and $({x}_{1},{y}_{1})$ is any point on the line.

Practice with our Point-slope form
exercise.

## What is standard form?

Standard form is yet another way to write a linear equation. The form is $Ax+By=C$ , where $A$ , $B$ , and $C$ are constants.

Practice with our Graph from linear standard form
exercise.

Practice with our Convert linear equations to standard form
exercise.

## Why might we rewrite a linear equation in a different form?

There are a few reasons we might choose to rewrite a linear equation in a different form. For example, if we're trying to graph the equation, slope-intercept form might be the easiest to work with. But if we're trying to solve a system of equations, standard form might be more useful. It really depends on the situation.

Practice with our Linear equations in any form
exercise.

## Want to join the conversation?

- how do we choose the point to base Point-slope form on(7 votes)
- From what I've seen, I don't think it matters. Whichever one is easiest, like a positive point is easier than a negative point in my opinion. Hopefully I understood your question. Have a great day!(19 votes)

- khan academy would be way better if they gave you a grilled cheese when you get an answer right just saying(5 votes)
- Your disposition exudes iPad kid energy.(14 votes)

- i dont like this(7 votes)
- Throughout the "Linear equations in any form" practice, I only used the slope intercept equation and the point-slope form equation. I didn't understand how to use standard form. How do you find A, B, and C in just one slope? What is A, B, and C? How do you use the standard form when breaking a slope into an equation? (Sry, that's a lot of questions)(4 votes)
- I like to keep my notation clear and label the forms as I use them. I also am developing a pattern to how I write out my info. So when it gives me two points on a graph and wants me to write an equation I'll write: (-2,-4)&(-5,5) do the rise over run etc.

x y .... x1, y1

To your question, you're reducing point slope form to slope intercept form. Use the Distributive property to move x to the other side. Don't think A,B,C Think x+y=b (b being x1 in the earlier equations which is also "b" in "y=mx+b"(0 votes)

- Are there any other applications for using the Standard Form aside from getting both x & y intercepts?(1 vote)
- Standard form of linear equations is also helpful for graphing, solving systems of equations, modeling real-world scenarios, matrix representation, and easier comparison of different equations.(0 votes)

- I have noticed that Standard Form was often mentioned alongside Systems of Equations, and I was wondering what a system of equations is. Thank you!(0 votes)
- how can i model supply and demand with linear equations any one hear to help(0 votes)
- Ok so y=mx+b and ax+by=c (standard form are interconnected) as is y-y₁=m(x-x₁) (point slope form)...... Like (3,4)and (-2,5) so lets say we want to write it in standard form and get the y intercept out of just this! Then, we first slope, my using y2-y1/x2/x1 The slope formula! And we get a slope of:

is -1/5 and then its y=-1/5x+b and we don't have y intercept right? Well now lets use y-y₁=m(x-x₁) and subsitue any of the points and then you hav'e point slope form! Editing the slope form ea'sil gives you ax+bx=c(0 votes)