Question

Write an equation of a line that passes through the point (7, 3) and is parallel to the line y = negative 2 over 3 x + 3.

Answer 1

We are asked to determine the equation of a line that is parallel to:

`y=-(2)/(3)x+3`

Two lines are parallel if their slopes are in the following relationship:

`m_2=-(1)/(m_1)`

Therefore, if m1 is the slope of the given line and m2 is the slope of the parallel line we may determine the value of the slope of the parallel line by replacing it in the relationship. Let's remember that when a line is written in the form:

`y=mx+b`

Where "m" is the slope. Therefore, m1 is -2/3. Replacing in the relationship we get:

`m_2=-(1)/(-(2)/(3))=(3)/(2)`

Now, we go back to the general form of a line equation and replace the value of the new slope:

`y=(3)/(2)x+b`

The value "b" is the y-intercept and can be found using the point through which the line passes:

`3=(3)/(2)(7)+b`

Now we solve the operations:

`3=(21)/(2)+b`

Subtracting 21/2 from both sides:

`3-(21)/(2)=b`

Solving the operations:

`-(15)/(2)=b`

Now we replace in the line equation:

`y=(3)/(2)x-(15)/(2)`

And thus we get the equation of the parallel line.