Answer:
The equation of the line that passes through the points (0, 3) and (5, -3) is [tex]y = -\frac{6}{5}\cdot x +3[/tex].
Step-by-step explanation:
From Analytical Geometry we must remember that a line can be formed after knowing two distinct points on Cartesian plane. The equation of the line is described below:
[tex]y = m\cdot x + b[/tex] (Eq. 1)
Where:
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
[tex]m[/tex] - Slope, dimensionless.
[tex]b[/tex] - y-Intercept, dimensionless.
If we know that [tex](x_{1},y_{1}) = (0,3)[/tex] and [tex](x_{2},y_{2})=(5,-3)[/tex], the following system of linear equations is constructed:
[tex]b = 3[/tex] (Eq. 2)
[tex]5\cdot m + b = -3[/tex] (Eq. 3)
The solution of the system is: [tex]b = 3[/tex], [tex]m = -\frac{6}{5}[/tex]. Hence, we get that equation of the line that passes through the points (0, 3) and (5, -3) is [tex]y = -\frac{6}{5}\cdot x +3[/tex].
