Write the parametric equation of the line 10x-4y=20

x = 1 - t and y = -2.5 - 2.5t.

Step-by-step explanation:

Parametric equations are the equations in which the all the variables of the equation are written in terms of a single variable. For example in 2-D plane, the equation of the line is given by y=mx+c, there x is the independent variable, y is the dependent variable, m is the slope, and c is the y-intercept. The equation of the given line is 10x - 4y = 20. The goal is to convert the variables x and y in terms of a single variable t. First of all, take two points which lie on the line. By taking x=1, y comes out to be -2.5 and by taking x=0, y comes out to be -5. The general form of the straight line is given by:

(x, y) = (x0, y0) + t(x1-x0, y1-y0), where (x, y) is the general point, (x0, y0) is the fixed point, t is the parametric variable, and (x1-x0, y1-y0) is the slope.

Let (x0, y0) = (1, -2.5) and (x1, y1) = (0, -5). Substituting in the general equation gives:

(x, y) = (1, -2.5) + t(-1, -2.5). This implies that x = 1 - t and y = -2.5 - 2.5t!!!