A clarification on linear equations and slope intercept form

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Amardeep

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While going through Khan Academy's session on Linear equations I came across these two statements
Intro to Slope Intercept Form

The following is a Slope intercept form of linear equation
y=2x+1

The following is not a linear equation in slope-intercept form
x=4y−7

Now the second equation can be rewritten as y = (x+7) / 4

and we know that x and y are just variables, which can be replaced by anything, say a and b or p and q.

So the question is why is y=2x+1 a slope intercept while x=4y−7 is not?
 
Amardeep said:
While going through Khan Academy's session on Linear equations I came across these two statements
Intro to Slope Intercept Form

The following is a Slope intercept form of linear equation
y=2x+1

The following is not a linear equation in slope-intercept form
x=4y−7

Now the second equation can be rewritten as y = (x+7) / 4

and we know that x and y are just variables, which can be replaced by anything, say a and b or p and q.

So the question is why is y=2x+1 a slope intercept while x=4y−7 is not?
Click to expand...
x = 4y -7 can be TRANSFORMED into slope-intercept form.

However, AS WRITTEN, it is NOT in slope-intercept form.
 
Amardeep said:
While going through Khan Academy's session on Linear equations I came across these two statements
Intro to Slope Intercept Form

The following is a Slope intercept form of linear equation
y=2x+1

The following is not a linear equation in slope-intercept form
x=4y−7

Now the second equation can be rewritten as y = (x+7) / 4

and we know that x and y are just variables, which can be replaced by anything, say a and b or p and q.

So the question is why is y=2x+1 a slope intercept while x=4y−7 is not?
Click to expand...
The key word here is form. The slope-intercept form is a particular form in which the equation can be written, namely y = mx + b. It must be solved for y, in particular (that is, written to show y as a function of x), and with no parentheses. Some people might even require two terms in that order, and reject y = 1 + 2x or y = 2x, but I don't consider that essential.

Equivalent equations will represent the same line, but in a different form.
 
The key word here is shape. The slope detection form is a special form for which the equation can be written, namely y = mx + b. It needs to be solved for y to be more precise (that is, written to display y as a function of x) and without the brackets. Some people might even need two terms on this line and reject y = 1 + 2x or y = 2x, but I don't think that matters.

SPAM website
 
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There are other useful forms of the linear equation:

Ax + By + C = 0

x/D + y/G = 1

Where A, B, C, D & G are constants.
 
HenryTorres said:
The key word here is shape. The slope detection form is a special form for which the equation can be written, namely y = mx + b. It needs to be solved for y to be more precise (that is, written to display y as a function of x) and without the brackets. Some people might even need two terms on this line and reject y = 1 + 2x or y = 2x, but I don't think that matters.
Click to expand...
Your response is a paraphrasing of response #4.

The referenced web article is a spam. Please do not repeat!
 
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