Answer: the equation ax + by = c represents a linear equation with x and y as variables. The coefficients a and b determine the slope, while the constant c determines the y-intercept of the line formed by the equation.
Step-by-step explanation: The equation ax + by = c represents a linear equation in two variables, x and y.
Here's a breakdown of the equation:
1. "a" and "b" are coefficients: They represent the constants multiplied by x and y, respectively. These coefficients determine the slope of the line formed by the equation.
2. "c" is a constant: It represents the value on the other side of the equation. This constant determines the y-intercept of the line formed by the equation.
To graph this equation, you can follow these steps:
1. Rewrite the equation in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
2. Determine the slope by dividing -a by b: m = -a/b. This will give you the slope of the line.
3. Identify the y-intercept by taking the value of c and dividing it by b: b = c/b. This will give you the point where the line crosses the y-axis.
4. Plot the y-intercept on the graph.
5. Use the slope to find another point on the line. Starting from the y-intercept, move horizontally by 1 unit and vertically by the value of the slope to find a second point.
6. Draw a straight line passing through the two points. This line represents the graph of the equation ax + by = c.