Answer:
The equation that represents a line that passes through the point [tex](6, -3)[/tex] and is parallel to [tex]y = 3\cdot x +1[/tex] is [tex]y = 3\cdot x -21[/tex].
Explanation:
According to the Analytical Geometry, a line is defined by the following expression:
[tex]y = m\cdot x + b[/tex] (1)
Where:
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
[tex]m[/tex] - Slope, dimensionless.
[tex]b[/tex] - Intercept, dimensionless.
By definition of the equation of the line, we understand that two lines that are parallel to each other has the same slope. Hence, the slope of the resulting line is:
[tex]m = 3[/tex]
If we know that [tex]x = 6[/tex], [tex]y = -3[/tex] and [tex]m = 3[/tex] , then the intercept of the parallel line is:
[tex](3)\cdot (6)+ b = -3[/tex]
[tex]18+b = -3[/tex]
[tex]b = -21[/tex]
Hence, the equation that represents a line that passes through the point [tex](6, -3)[/tex] and is parallel to [tex]y = 3\cdot x +1[/tex] is [tex]y = 3\cdot x -21[/tex].
