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Answer:
Step-by-step explanation:
In order to find the equations that are parallel/perpendicular to the line , we need to note a couple things about the relationships between lines and their parallel/perpendicular lines.
- A) If a line is perpendicular to another, the slopes will be opposite reciprocals (for instance
and
- multiplied, they equal -1.)
- B) If a line is parallel to another, they will have the exact same slope.
We know that the slope of a perpendicular line will be the the opposite reciprocal of the line we're comparing it to.
Since the slope of our base line is , we can find the reciprocal, then the opposite of that.
- Reciprocal of
- Opposite of
So the slope of this line will be , making our equation
However, y-intercepts will not stay the same. In order to find this, we can substitute the point (4, 2) into our equation to solve for b.
Now we know the y-intercept of this equation is . We can now finish off our equation of the line by substituting that in to what we already have,
.
As mentioned earlier, parallel lines will have the exact same slope but not the same y-intercept. Since the slope of our original equation is , the slope for this one will also be
.
So we now know the equation looks something like .
In order to solve for b, we apply the same logic we did in the perpendicular line and substitute in the point (4, 2) into the equation.
Now that we know the slope and the y-intercept, we can finish off our equation as .
Hope this helped!