Final answer:
To find a set of parametric equations for a given line, we need to calculate the slope and y-intercept of the line. Then, we can formulate the equations using the parameter t. For example, if we have two points on the line, we can find the slope and y-intercept using the formula y = mx + b. Finally, we can substitute these values into the parametric equations x = t and y = mt + b.
Step-by-step explanation:
Linear Equation and Scatter Plot
To find a set of parametric equations for a given line, we need the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. If we have two points on the line, say (x₁, y₁) and (x₂, y₂), we can find the slope by using the formula: m = (y₂ - y₁) / (x₂ - x₁). Then, we can substitute the values of m and b into the parametric equation: x = t and y = mt + b, where t is a parameter.
Example:
Let's say we have two points on the line: (2, 3) and (4, 7). The slope (m) can be calculated as: m = (7 - 3) / (4 - 2) = 2. The y-intercept (b) can be found by substituting one of the points into the slope-intercept form: 3 = 2(2) + b, which gives us b = -1. Therefore, the parametric equations for the line are: x = t and y = 2t - 1.