Question

Which equation represents a line that passes through the point (6,-3) and is parallel to the graph to y= 3x + 1?

Answer 1

The equation that represents a line that passes through the point
`(6, -3)` and is parallel to
`y = 3\cdot x +1` is
`y = 3\cdot x -21`.

Step-by-step explanation:

According to the Analytical Geometry, a line is defined by the following expression:

`y = m\cdot x + b` (1)

Where:

`x` - Independent variable, dimensionless.

`y` - Dependent variable, dimensionless.

`m` - Slope, dimensionless.

`b` - 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:

`m = 3`

If we know that
`x = 6`,
`y = -3` and
`m = 3` , then the intercept of the parallel line is:

`(3)\cdot (6)+ b = -3`

`18+b = -3`

`b = -21`

Hence, the equation that represents a line that passes through the point
`(6, -3)` and is parallel to
`y = 3\cdot x +1` is
`y = 3\cdot x -21`.