<p>I got it right on the test, by a guess haha. Please explain it for me? thank you in advance</p>
<p>In the xy-plane line L passes through the points (4,4) and (9,6). What is the x- intercept of the line L</p>
<p>You’d want to find the equation for the line. So do rise over run to find the slope:
(6 - 4)/(9-4) = 2/5 = .4
Then plug in one of the points to find the full equation:
4 = .4(4) + b
4 = 1.6 + b
-1 .6 -1.6</p>
<hr>
<p>b = 2.4</p>
<p>Final equation: y = .4x + 2.4, then you just set y = 0 and solve:
0 = .4x + 2.4
-2.4 -2.4
-2.4 = .4x</p>
<h2>/.4 /.4</h2>
<p>x = -6</p>
<p>X interception: (-6,0)</p>
<p>Then again I suck at math so this could be wrong :)</p>
<p>All you have to know is the basic equation for a line, which is:</p>
<p>f(x) = mx + b</p>
<p>f(x) is the same thing as y, so you might have also seen it written as: </p>
<p>y = mx + b</p>
<p>In these equations, m is the slope of the line, and b is the y-intercept</p>
<p>Actually, I lied. You also need to know how to get the slope of a line, which you do by plugging the respective points into the equation:</p>
<p>(y2 - y1) / (x2-x1) AKA: rise/run</p>
<p>Then, just plug in the points given. Here’s what would be on my paper:</p>
<p>(6-4)/(9-4) = 2/5
m = 2/5
6= (2/5)(9) + b
6= 18/5 + b
b = 12/5
y = (2/5)x + 12/5 <-------------------- This is the equation of the line</p>
<p>The x-intercept is the point where y = 0, so plug that into the equation you just derived.</p>
<p>0 = (2/5)x + 12/5
-12/5 = (2/5)x
(-12/5)(5/2) = x
(-60/10) = x
x = -6</p>
<p>Your answer is -6 </p>
<p>This is actually a really simple problem, but I wrote out the entire thought process and all the steps for you. You could also use point-slope form instead of y = mx + b.</p>
<p>As is so often the case, a neat diagram will solve this with minimal math in about 20 seconds. Seriously, you just have to try this:</p>
<p>Draw the picture NEATLY. You’ll see that to go from one point to the other you have to go up 2 and over 5. So to get back to the X axis, you need to go down 2, left 5 and then down 2 more, left 5 more. So overall, you have gone 10 units to the left, starting from +4 which means you have landed at (-6,0).</p>
<p>And as also is often the case, you could object that my method only works when the numbers are “nice”. But the funny thing about the SAT is that the numbers always seem as if they were chosen to reward lazy people like me (and my students) :)</p>
<p>I remember that question. I did what those guys did above.</p>
<p>You don’t even need a formula to do that. From 9,6 to 4,4, x decrease by 5 when y decrease by 2. To get the x-axis intercept when y=0, just need to find how much more x needs to go down when y drops by another 4 (which is 10). 4-10=-6. Finish in 5 seconds.</p>