Write an equation in slope intercept form that passes through (-4,7) and is perpendicular to y+4=1/4(x-7)
Let's break this down into a few parts first.
Slope intercept form is otherwise known as y = mx + b, where m is the slope and b is the y-intercept.
Perpendicular means that the two lines will intersect each other at a 90 degree angle. In math terms, their slopes will be negative reciprocals of each other.
Starting with y + 4 = 1/4(x -7), putting into slope intercept form, y = mx + b, m = 1/4 and b=-7/4 -4.
Since it is perpendicular, it must have a slope that is a negative reciprocal. The slope of the original line is 1/4, so the multiplying it -1, we get -1/4, and taking the reciprocal, we get -4. So the slope of the perpendicular line is -4.
So, y = -4x + b, but we don't know what the value of b is. To determine this, we know the point (-4,7) is on the line that we are trying to find, so we can substitute it into the equation and calculate b to make it work.
Every time we see an x we put in -4 and every time we see a y, we put in 7.
y = -4x + b
7 = -4(-4) + b
7 = 16 + b
subtract 16 from both sides
7 - 16 = 16 + b - 16
-9 = b
Now substitute this into the equation.
y = -4x + -9
Putting it into correct form, we get y = -4x - 9.
Let's check it to see if it is correct.
It has a slope of -4, so it is perpendicular to y=1/4x - 5 3/4.
Is the point (-4,7) on the line? Let's substitute it in to see if it is on the line.
Again, everywhere we see an x, we put in -4 and everywhere we see a y we put in 7.
y= -4x - 9
7 = -4 (-4) - 9
7 = 16 - 9
7 = 7
Sorry for the very long explanation, I was being overly thorough, but after you do a few of them, you will be able to knock them off in minutes.
Apr 03, 2016 |
Office Equipment & Supplies