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sahilmm15
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How does a,b,c effects the equation ax+by=c graphically. Thanks!
Write it as ##\begin{bmatrix} a & b \end{bmatrix} \cdot \begin{bmatrix} x \\ y \end{bmatrix}=c ## and ask again. What does ##c=0 ## and ##c\neq 0## mean, and what stands ##(a,b)## for?sahilmm15 said:How does a,b,c effects the equation ax+by=c graphically. Thanks!
If a = 0 and b = 0, the equation is 0x + 0y = c. What can you say about c? Does this equation have any solutions?sahilmm15 said:How does a,b,c effects the equation ax+by=c graphically. Thanks!
The value of a in the equation ax+by=c affects the slope of the graph. A larger value of a will result in a steeper slope, while a smaller value of a will result in a flatter slope. If a is negative, the graph will be reflected across the x-axis.
The value of b in the equation ax+by=c affects the y-intercept of the graph. A larger value of b will result in a higher y-intercept, while a smaller value of b will result in a lower y-intercept. If b is negative, the graph will be reflected across the y-axis.
The constant term c in the equation ax+by=c affects the position of the graph on the coordinate plane. It represents the point where the graph intersects the y-axis when x=0. So, a larger value of c will shift the graph up, while a smaller value of c will shift the graph down.
When all three variables, a, b, and c, are changed, the graph will undergo a transformation. The slope, y-intercept, and position on the coordinate plane will all be affected. For example, changing a and b while keeping c constant will result in a different slope and y-intercept, but the graph will still intersect the y-axis at the same point.
Yes, the graph of ax+by=c can be a straight line. This will occur when either a or b is equal to 0, resulting in a horizontal or vertical line, respectively. It can also be a straight line when a and b are both non-zero, but their ratio is constant.