Here’s the question: “Write the equation of the line perpendicular to AD (The Slope-intercept of AD is y+=/x-/) through the point B ( , ).
I feel like I’m reading an extinct language. Can someone help me, here?
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First, fully convert equation of line AD to slope-int. form.
y = m(slope)*x +b(y coordinate of y-intercept (, y)) or simply,
y = mx +b
y+=/x-/
y = /x -/ –
y = /x -/ -/
y = /x -/ [slope=/, y-int.= -/]
Look at this line on the graph below. Notice where it crosses the y-axis.
Look at the slope of the line. It should be going up because m is positive.
Take the negative reciprocal of m (/) to make a perpendicular slope (-/).
Plug in (, ) & -/ into your equation to find b and make the new line equation.
y = mx +b
= (-/) +b
= -/ +b
-(-/) = b
/ +/ = b
/ = b [leave it as an improper fraction; make your perp. equation]
y = -/x +/ [notice how denominators for m & b are the same]
If you understand what is going on, you’ll know which line is which.
Use mouse to move cursor and change lines and scale of graph.
Find: (,), & both y-intercepts.
Keep playing until you understand this new “language.”
Source(s): http://www.google.ca/#hl=en&gs_rn=&gs_ri=psy-ab&…
The question is gobbledygook. That might be why you have trouble understanding it. That equation is not “slope-intercept”, it is just a mishmash. However, it is possible to pick out the slope, which is the only thing you need from it. The slope is /. A perpendicular has the negative reciprocal slope, -/.
The equation of a line is y = mx where m is the slope. That line passes through the origin. If you want it to pass through a point (j, k) you subtract the coordinates: y – k = m(x – j). This form of equation is called point-slope. You can rewrite it in the form y = mx + b and that is called slope-intercept. So let’s write our equation.
y – = (-/)(x – ) Notice that I type the slope differently from the equation mentioned in the problem. That equation is ambiguous. You can’t tell if it should be /(x) or (/)x. You can not stand an ambiguous statement in math. Every statement must have exactly one way to interpret it.
So there is the answer. You can rewrite it if that would be convenient.
y – = -x/ + /
y = -x/ + / Slope-intercept form. That means when x = the line crosses the y axis at /.
BTW It does not matter what point you use to write a point-slope equation as long as it is actually on the line. They all resolve to the same answer.
The slope of y+=(/)x-(/) is /. So any perpendicular line is going to have a slope of -/.
The equation of a line is y = mx+b where m is the slope and b is the y-intercept. So, using the point (,), we have
= (-/)* + b
b = .
So the perpendicular line is
y = (-/)x + /
I hope that helps!