<p>Hey so okay... this is from the collegeboard's book. Test 3, Section 2, page. 522, question 17.</p>
<p>In the xy-plane, line l passes through the origin and is perpendicular to the line 4x + y = k, where k is a constant. If the two lines intersect at the point (t, t + 1), what is the value of t?</p>
<p>go for it!</p>
<p>You won't get a response for a while, as hundreds of nerdy CCers are AXIOUSLY pressing the refresh button on collegeboard.com to get their SAT scores, while praying that colleboard somehow releases the scores before the 04/11 8:00 A.M. release date :)</p>
<p>rearrange 4x+y=k to get y=-4x+k
that means the slope of the line going through the origin is 1/4 and the equation for that line is y=x/4
then you replace y with t+1 and x with t and solve for t
and you get -4/3</p>
<p>t=-4/5? Is my brain fried or whaT?</p>
<p>that's not even one of the answer choices</p>
<p>The second line's equation can be rewritten as y = -4x + k Thus, the slope is negative 4. So a line perpendicular to this would have a slope that is its negative reciprocal or positive 1/4. Now you can write that line's equation as y= (1/4) x. Here there is no b or y intercept because the y intercept is zero (it passes through the origin). Now that you know that the two lines intersect, that is where the two functions are equal to each other. So let
-4x + k = (1/4) x Solving for k, you get 4k = 17x, so k = (17/4) x. Since x = t, and y = t +1, when we substitute in the equation y = (1/4) x, we get t +1 = (1/4) t; Solving for t you get t = negative 4/3. Thus, x is negative 4/3, and y is negative 1/3. So you see that the equation holds up for y=(1/4) x as neg. (1/3) = (1/4) x (-4/3) and the equation y = -4x + k holds up as well. Remember that I said k = (17/4)x so the equation is really now
y = -4x + (17/4)x. So substitute our newfound values of x = (-4/3) and y = (-1/3) The equation becomes (-1/3) = -4(-4/3) + (17/4)(-4/3) which is (16/3)+ (-17/3) = (-1/3). So ultimately, t = -4/3 and t + 1 = -1/3.
Does that help?????</p>
<p>When I mentioned b, i was talking about the b in the slope intercept form of y = mx + b</p>