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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?
I just made y the subject so thatNidum said:What ways of rearranging Ax + By + C = 0 into the form y= mx + b have you tried ?
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.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?
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.
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.
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.
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.
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.