Write an equation in standard form given slope intercept form

To avoid this vicious circle certain concepts must be taken as primitive concepts; terms which are given no definition. When the line concept is a primitive, the behaviour and properties of lines are dictated by the axioms which they must satisfy. In a non-axiomatic or simplified axiomatic treatment of geometry, the concept of a primitive notion may be too abstract to be dealt with. In this circumstance it is possible that a description or mental image of a primitive notion is provided to give a foundation to build the notion on which would formally be based on the unstated axioms.

The equation must be simplified, which means all numbers must be integers that do not share a common factor other than one. Alright, we'll worry about this second part in a little bit.

Let's see if we can rewrite this. Let me get my scratch pad out. So the way that it's written right now, this is slope intercept form. It's very easy to figure out what the slope and what the Y intercept is from this equation.

But we wanna write this in standard form. Which would be the form Ax plus By is equal to C. And that extra text they were saying, the equation must be simplified. Which means all numbers must be integers that do not share a common factor other than one.

That just means that A, B, and C in the standard form they want need to be integers. And they want them to not have any common factors. So if we got to the point of say 4x plus 2y is equal to 10, well this number, and this number, and this number are all divisible by two. They all have the common factor of two.

So we would want to simplify it more. Divide them all by two and then you would get two so you divide this by two. You get 2x, divide this by two you'll get plus y is equal to 5.

So this is the form that they're asking for and probably because it's just easier for the site to know that this is the right answer. Because there's obviously a bunch of forms in this way.

So let's see if we can do that. Let's see if we can write it in standard form.

So the first thing I would wanna do is, well there's a bunch of ways that you could approach it. The first thing you could try to do is well let's get rid of all of these fractions. And the best way to get rid of the fractions is to multiple by three and to multiply by seven.

If you multiply by three you get rid of this fraction.

Standard form

If you multiply by seven you get rid of this fraction. So if you multiply three and you multiply by seven. Let me just rewrite it over here. There's actually also a couple of ways that we can do this.

So if you multiply. So one way to do it. So if I multiply this side by three and I multiply by seven, I have to do that to this side as well.Linear equations can take several forms, such as the point-slope formula, the slope-intercept formula, and the standard form of a linear equation.

These forms allow mathematicians to describe the exact same line in different ways. You can find the straight-line equation using the point-slope form if they just give you a couple points: Find the equation of the line that passes through the points (–2, 4) and (1, 2).

I've already answered this one, but let's look at the process. Regents Prep is an exam prep course and online learning center designed to help students pass their exams, become certified, obtain their licenses, and start their careers.

Example 1: Writing an Equation Given Two Points

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Equations that are written in slope intercept form are the easiest to graph and easiest to write given the proper information. All you need to know is the slope (rate) and the y-intercept. Sal finds the equation of a line that passes through (-3,6) and (6,0) in point-slope, slope-intercept, and standard form.