Question

What is the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10?

Answer 1

What you should do first is simplify the equation into the y = mx + b format. Move 2x to the other side. Know that in doing this, 2x must become the opposite of what it currently is (-2) in order for the equation to remain true. We also have to take away the '10' because the line is parallel, not exactly the same, which means a different y intercept. This looks like:

$5y = -2x + b$

Next, simplify y to make things easier. This can be done by dividing both sides by 5, like so:

$\frac{5}{5}y = -\frac{2}{5}x + b$

What you should also know is that if a line is parallel to another, then this means the slope has to be the same because they both have the same changes in rise and run. With this in mind, simply plug in the x and y values.

$(-4) = -\frac{2}{5} * (5) + b$

$--> -4 = \frac{10}{5} + b$

$---> -4 = -2 + b$

Add 2 to both sides to isolate b.

$-4 + 2 = b$

Which means that -2 = b.

Now that we have the y intercept, we can write the equation of the line, which is $y = -\frac{2}{5}x - 2$.

Hope this was helpful.