Line Equations: Rearranging Ax + By + C = 0 to y=mx+b

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In summary, the conversation discusses how to rearrange the general line equation of Ax + By + C = 0 into the slope-intercept form of y = mx + b. It is noted that vertical lines cannot be written in this form since their slope is undefined. However, any other non-vertical line can be expressed in either form. The individual has tried making y the subject but is unsure if it is correct. It is also mentioned that all allowed operations can be performed on equations.
  • #1
Einstein's Cat
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Say a line equation is expressed with the General equation of Ax + By + C = 0; can one just simply rearrage this into the form of y= mx + b?
 
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  • #2
What ways of rearranging Ax + By + C = 0 into the form y= mx + b have you tried ?
 
  • #3
Nidum said:
What ways of rearranging Ax + By + C = 0 into the form y= mx + b have you tried ?
I just made y the subject so that
Y= (-a/-b)x + (-c/-b); this may not be correct, I've just done it now
 
  • #4
You can simplify the expression.
It doesn't work if b=0.

You can always perform all allowed operations on equations.
 
  • #5
Einstein's Cat said:
Say a line equation is expressed with the General equation of Ax + By + C = 0; can one just simply rearrage this into the form of y= mx + b?
Vertical lines such as x = 2 are special cases of the general equation (A = 1, B = 0, C = -2), but can't be written in the slope-intercept form, since the slope is undefined. Any other line that isn't vertical can be written in either equation form.
 

1. What is the purpose of rearranging a line equation to the form y=mx+b?

Rearranging a line equation to the form y=mx+b allows us to easily identify the slope of the line (m) and the y-intercept (b). This form is also known as the slope-intercept form and is useful in graphing and solving equations.

2. How do you determine the slope of a line from the equation Ax + By + C = 0?

The slope (m) of a line can be determined by rearranging the equation to the form y=mx+b and then identifying the coefficient of x. The slope is then equal to -A/B.

3. Can a line equation be rearranged to the form y=mx+b if it is in a different form?

Yes, any linear equation can be rearranged to the form y=mx+b by isolating the y variable on one side of the equation and simplifying the other side. This can be done for equations in standard form, point-slope form, or slope-intercept form.

4. How does changing the values of A, B, and C affect the line equation?

The values of A, B, and C in the equation Ax + By + C = 0 affect the slope and y-intercept of the line. Changing the values of A and B will change the slope, while changing the value of C will change the y-intercept. The overall shape and direction of the line will also be affected.

5. Can the line equation y=mx+b have a negative slope?

Yes, the slope (m) of a line can be positive or negative, depending on the values of A and B in the equation Ax + By + C = 0. A negative slope indicates that the line is decreasing from left to right on a graph, while a positive slope indicates that the line is increasing from left to right.

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