Forms of linear equations review (article) | Khan Academy (2024)
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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Kelsen Miener
7 years agoPosted 7 years ago. Direct link to Kelsen Miener's post “In the point slopes form,...”
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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(19 votes)
Scott Ferguson
4 years agoPosted 4 years ago. Direct link to Scott Ferguson's post “That is correct. You can ...”
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.
(43 votes)
Betsy Glad
3 years agoPosted 3 years ago. Direct link to Betsy Glad's post “How do you know when to u...”
How do you know when to use point slope form vs slope intercept form?
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(16 votes)
Kim Seidel
3 years agoPosted 3 years ago. Direct link to Kim Seidel's post “Most of the time, it woul...”
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.
3 years agoPosted 3 years ago. Direct link to ZetaFox's post “ax + by + c = 0ax + by =...”
ax + by + c = 0 ax + by = c
I'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)
Khushi Viramgami
3 years agoPosted 3 years ago. Direct link to Khushi Viramgami's post “hey! okay, so I'm pretty ...”
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!!
(19 votes)
victoria.reed
7 years agoPosted 7 years ago. Direct link to victoria.reed's post “when do you need to use s...”
when do you need to use slope?
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(11 votes)
James Gallagher
a year agoPosted a year ago. Direct link to James Gallagher's post “To determining the slope/...”
To determining the slope/ steepness of a line. You should review the slope videos if you need help.
(2 votes)
Corey Zuk
3 years agoPosted 3 years ago. Direct link to Corey Zuk's post “i must be behind in math ...”
i must be behind in math because all of this is way too confusing
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(8 votes)
em
4 years agoPosted 4 years ago. Direct link to em's post “Why are point-slope opera...”
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)?
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(4 votes)
Kim Seidel
4 years agoPosted 4 years ago. Direct link to Kim Seidel's post “Point slope form is a var...”
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)
worldsage
7 years agoPosted 7 years ago. Direct link to worldsage's post “Is it possible to convert...”
Is it possible to convert standard form back to point-slope directly?
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(5 votes)
mickycarey
9 months agoPosted 9 months ago. Direct link to mickycarey's post “In the previous exercise:...”
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)
Kim Seidel
9 months agoPosted 9 months ago. Direct link to Kim Seidel's post “You would need to use poi...”
You would need to use point-slope form or slope intercept form to create an equation. Then, convert it to standard form.
(6 votes)
Stelios Kourentzis
4 years agoPosted 4 years ago. Direct link to Stelios Kourentzis's post “at the end it says this i...”
at the end it says this is a standard form y+3x=−10 it sould be fist 3x +y= -10 isn't ?
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(4 votes)
Peter Dresslar
3 years agoPosted 3 years ago. Direct link to Peter Dresslar's post “Specifically there are a ...”
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)
ultraidiotboy
3 years agoPosted 3 years ago. Direct link to ultraidiotboy's post “what’s point-slope form g...”
what’s point-slope form going to be useful for?
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(4 votes)
etoile~
3 years agoPosted 3 years ago. Direct link to etoile~'s post “Point slope form is impor...”
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. 🙃
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.
To solve linear equations, find the value of the variable that makes the equation true. Use the inverse of the number that multiplies the variable, and multiply or divide both sides by it. Simplify the result to get the variable value. Check your answer by plugging it back into the equation.
There are three types of linear equations: standard form ( A x + B y = C ), slope-intercept form ( y = m x + b ), and point-slope form ( y − y 1 = m ( x − x 1 ) ). In standard form, , , and are integers, and either an or a must be present, meaning only one variable can be included in the standard form of an equation.
As there are many ways to solve linear equations, mathematicians may wonder about efficiency, the advantages, and the disadvantages of each method. Reviewing the research done by other experts, we choose to focus on three main techniques: Eliminating variables, Cramer's rule, and Gaussian Elimination.
Put students into pairs and show an equation on the board. Have one student instruct the other on how to solve as the student listening writes each step and solution. Then, show a new equation and have students switch roles. This gives students a chance to teach and reinforce what they remember about linear equations.
The standard form of a linear equation is Ax+By=C. A, B, and C are constants, while x and y are variables. Standard form lets us quickly find the x- and y- intercepts.
A linear equation is an equation where the unknowns or variables are powers with exponent one. For example, 3x - 4y + 5z = 3 is a linear equation because the variables x, y, z are linear, but xy + 3z = 7 is not linear because of the term xy, which is a product of two variables.
A linear function refers to when the dependent variable (usually expressed by 'y') changes by a constant amount as the independent variable (usually 'x') also changes by a constant amount. For example, the number of times the second hand on a clock ticks over time, is a linear function.
Different forms of linear equations are important because each form reveals a certain amount of information about the line. For example the slope intercept form reveals the slope and.
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