Final answer:
The equation ax + by = c describes a straight line with varying position and slope depending on the coefficients a, b, and c. The slope is represented by -(a/b) and the y-intercept by (c/b). The line can slope upward, be horizontal, or slope downward based on the value of b.
Step-by-step explanation:
The graph of the equation ax + by = c represents a straight line in a two-dimensional Cartesian coordinate system. Depending on the values of a, b, and c, the position and slope of this line can vary. If we solve the equation for y, we get y = -(a/b)x + (c/b), which is similar to the general form of a straight line equation y = mx + b, where m represents the slope and b represents the y-intercept.
For different values of b:
- If b > 0, the line slopes upward to the right.
- If b = 0, the line is horizontal, which occurs only when the coefficient of x is zero.
- If b < 0, the line slopes downward to the right.
The slope of the line is determined by the ratio -(a/b), which indicates the rise over run or the amount the line goes up (or down) for a one-unit horizontal change. The y-intercept is the point where the line crosses the y-axis, which is calculated as c/b. Remember that the graph always has perpendicular axes, with the horizontal axis being the independent variable (x) and the vertical axis being the dependent variable (y).