There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form. We review all three in this article.

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In the point slopes form, it looks like you're saying you could use either set of coordinates.I thought it was the first set of coordinates since it says x1 and y1. Please explain. Thanks.

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(18 votes)

That is correct. You can definitely use either set of coordinates. Don't mix-and-match: you can't use x1 and y2, but you can use (x1, y1) or (x2, y2) and it will work just as well either way.

(37 votes)

How do you know when to use point slope form vs slope intercept form?

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(16 votes)

Most of the time, it would be your choice. Though, your teacher may request that you use a specific approach to see if you know how to do it.

ax + by + c = 0

ax + by = cI've heard of 2 "standard" forms of linear equations. Which one is correct?

should c in the 1st line be -c though? since im moving it from the right to left...?

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(9 votes)

hey! okay, so I'm pretty sure you're confusing a quadratic equation with a linear equation. A linear equation is a straight line, while a quadratic is a curve/parabola. You'll probably learn that later in algebra 1 and 2.

anyways, the standard linear equation is ax+by=c, while the standard quadratic equation is slightly different from what you have; it should be ax^2+bx+c=0

hope this helps!!

(17 votes)

when do you need to use slope?

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(11 votes)

To determining the slope/ steepness of a line. You should review the slope videos if you need help.

(2 votes)

Why are point-slope operations the opposite?

For example, the point is (2,-3).

why is y+3=3/4(x-2) correct but not y-3=3/4(x+2)?•

(4 votes)

Point slope form is a variation of the slope formula:

Slope m = (y2-y1)/(x2-x1)

If you mulitply both sides by (x2-x1), then you get point slope form:

(y2-y1) = m(x2-x1)

Then, they swab a couple of variables to clarify the variables that stay. X2 becomes X, and Y2 becomes Y. And, you have the point slope form.Remember, slope is calculated as the change in Y over the change in X. So, it requires the subtraction.

Hope this helps.

(8 votes)

i must be behind in math because all of this is way too confusing

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(7 votes)

at the end it says this is a standard form y+3x=−10

it sould be fist 3x +y= -10 isn't ?•

(4 votes)

Specifically there are a lot of teachers that would mark y+3x=−10 wrong. Maybe correctly; the form is the whole point of the exercise.

(2 votes)

In the previous exercise: "Linear equations in any form", is there a method to figure out from the graph the equation in standard form directly or do you have to work out one of the slope forms first and then re-arrange the formula?

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(4 votes)

You would need to use point-slope form or slope intercept form to create an equation. Then, convert it to standard form.

(5 votes)

what’s point-slope form going to be useful for?

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(4 votes)

Point slope form is important because it can give us another set of coordinate pairs when we are only given one. Using algebraic manipulation, you can find coordinates

*and*the slope from just that equation which helps with graphing. Being able to readily switch from different linear equation forms helps solving complex problems. Hope this helps. 🙃(5 votes)

Is it possible to convert standard form back to point-slope directly?

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(4 votes)

Certainly! The concepts revolving around linear equations include various forms used for different purposes in mathematics. Let's dive into the specifics mentioned in the discussion and provide insights into each concept:

### 1. **Point-Slope Form**:

**Description:**Point-slope form is expressed as (y - y_1 = m(x - x_1)), where (m) represents the slope of the line, and ((x_1, y_1)) denotes a point on the line.**Insights from the Discussion:****Kelsen Miener and Scott Ferguson:**Address the interchangeable use of coordinates ((x_1, y_1)) or ((x_2, y_2)) in the point-slope form.**em:**Discusses the reversal of operations in point-slope equations, exemplifying how (y+3 = \frac{3}{4}(x-2)) is correct while (y-3 = \frac{3}{4}(x+2)) is not due to the opposite nature of operations.

### 2. **Slope-Intercept Form**:

**Description:**Slope-intercept form appears as (y = mx + b), where (m) signifies the slope, and (b) denotes the y-intercept.**Insights from the Discussion:****Betsy Glad and Kim Seidel:**Inquire about choosing between point-slope and slope-intercept forms, highlighting that often, it's a matter of choice or might be specified by a teacher for particular exercises.

### 3. **Standard Form**:

**Description:**Standard form is represented as (Ax + By = C), where (A), (B), and (C) are constants, and (A) is non-negative.**Insights from the Discussion:****ZetaFox, Khushi Viramgami, Stelios Kourentzis, Peter Dresslar, and mickycarey:**Engage in discussions and queries regarding the correctness of standard form equations, sign placement, and rearrangement of terms.

### Additional Insights:

**Use of Slope:****victoria.reed and James Gallagher:**Address the use of slope in determining the steepness of a line and its importance in understanding linear equations.

**Utility of Point-Slope Form:****etoile~:**Highlights the significance of point-slope form in determining coordinates and slopes from a given equation, aiding in graphing and problem-solving.

### Conversions and Relations:

**Reverting from Standard Form to Point-Slope:****worldsage:**Raises the query of converting standard form back to point-slope directly, indicating a desire to understand the interconvertibility of different linear equation forms.

### Conclusion:

The conversation showcases queries, clarifications, and discussions regarding the use, understanding, and interrelations among point-slope, slope-intercept, and standard forms of linear equations. It also emphasizes the practical applications, choices in usage, and the significance of slope in comprehending linear relationships and graphing.