Question

Give an equation of a line that is parallel to −3x + 7y =4. Explain why your line is parallel to the given line and how you arrived at your answer.

Answer 1

3x -7y = 0

Explanation:

Parallel lines have the same slope.

Changing the constant in a linear equation like this only changes the y-intercept. It has no effect on the slope of the line. So, we can change the constant from 4 to 0 and we will have a line with the same slope, parallel to the original, but with a different y-intercept.

The "standard form" of the equation of a line has the leading coefficient positive. We can make that be the case by using the multiplication property of equality, multiplying both sides of the equation by -1.

Parallel line:

-3x +7y = 0

In standard form:

3x -7y = 0