<p>If the slope of the line that passes through the points (a,0) and (1,-2) is 1/2, what is the value of a? </p>
<p>Please show all your steps. I know this is really easy, but I don't understand what to do.</p>
<p>Use the formula y=mx+b.</p>
<p>Plug in (1, -2):
-2 = 1/2(1) + b
Now you know b.</p>
<p>You can plug in (a, 0) to calculate a, since you know the value of b.
0 = (1/2)a + b</p>
<p>You can use the formula for slope, m=change y/change x</p>
<p>1/2= (-2-0)/(1-a)
1/2=-2/(1-a)
1-a=-4
a=5</p>
<p>easily,
slope=(y2-y1)/(x2-x1)
then,
1/2=(-2-0)/1-a
1/2=-2/1-a
cross multiply:
1-a=-2*2
1-a=-4
-a=-5
a=5</p>
<p>There you go xD</p>
<p>While the method used by renoverchat (#2) is mathematically sound, the method used by RandomHSer and 2200 (#3 and #4) is quicker and much more direct.</p>
<p>The graphical method is the quickest in this case: </p>
<p>Plot the point (1,-2). Since the slope is 1/2 you can move up 1 and right 2 to get to another point on the line. Do this twice and you arrive at the point (5,0). So a=5.</p>
<p>I agree with Dr Steve. And it is suprising how often this method works. It seems less sophisticated and less math-y but drawing a neat diagram and counting boxes often leads to the solution with startling ease!</p>
<p>Yeah agreed, but not on SAT though- where there is no grid paper… 
But otherwise, it’s cool… But I think you should know how to “calculate” it cuz you’ll do it more often that way anyway…</p>