write the slope intercept form of the equation of the line described. through (2,-4), perpendicular y= 2/5x-4

Answer 1

There are 2 things you need to write an equation of a line: slope and y-intercept. In the equation given, the slope is 2/5. To find a perpendicular slope, you find the "opposite reciprocal", which means "flip and change the sign". With that said, your perpendicular slope is -5/2.

Using the perpendicular slope (m) and the ordered pair (x, y), plug those into y=mx+b and solve for b, which looks like this:

y=mx+b >>> -4=(-5/2)*(2)+b

Then use order of operations and properties of equations to solve for b:

-4=(-5/2)*(2)+b >>> -4=-5+b >>> 1=b. Your y-intercept is 1.

Finally, take your perpendicular slope and y-intercept and put it into y=mx+b. Your answer is:

y = -5/2 x + 1