Find the equation of the line through point (3,4) and perpendicular to y=−2x−4. Use a forward slash (i. e. "/") for fractions (e. g. 1/2 for 12). Y=

y = 1/2x + 5/2

Step-by-step explanation:

Remember that if a line is perpendicular to another line, they intersect, and create a 90 degree angle. Because of this, we know that their slopes cannot be the same. In fact, to find a perpendicular line, you must find the Negative Reciprocal of the given line's slope.

A negative reciprocal of -2, would be positive 1/2.

So, this is the slope of the line perpendicular to y = 2x-4.

You're given a point that this line passes through, however you need the Y-Intercept. Thus, you must plug in the point to the slope formula.

You should have: 4 = 1/2(3) + b

Now we solve for b.

4 = 3/2 + b

Subtract 3/2 from both sides

5/2 = b

Now that we have our y-intercept we can finish writing the equation for the line perpendicular by simply taking out the points we plugged in. Leave the slope however.

Y = 1/2x + 5/2