You want to find the equation for a line that passes through the two points:
(100,19) and (250,17).
First of all, remember what the equation of a line is:
y = mx+bWhere:<span>m is the slope, andb is the y-intercept</span>
First, let's find what m is, the slope of the line...
<span>The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (100,19), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=100 and y1=19.Also, let's call the second point you gave, (250,17), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=250 and y2=17.Now, just plug the numbers into the formula for m above, like this:<span>m=<span>17 - 19250 - 100</span></span>or...<span>m=<span>-2150</span></span>or...<span>m=-1/75</span>So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:<span>y=-1/75x+b</span></span>Now, what about b, the y-intercept?
<span>To find b, think about what your (x,y) points mean:<span><span>(100,19). When x of the line is 100, y of the line must be19.</span><span>(250,17). When x of the line is 250, y of the line must be17.</span></span>Because you said the line passes through each one of these two points, right?Now, look at our line's equation so far: <span>y=-1/75x+b</span>. b is what we want, the -1/75 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (100,19) and (250,17).So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.You can use either (x,y) point you want..the answer will be the same:<span><span>(100,19). y=mx+b or 19=-1/75 × 100+b, or solving for b: b=19-(-1/75)(100). b=61/3.</span><span>(250,17). y=mx+b or 17=-1/75 × 250+b, or solving for b: b=17-(-1/75)(250). b=61/3.</span></span>See! In both cases we got the same value for b. And this completes our problem.<span><span>The equation of the line that passes through the points(100,19) and (250,17)is</span><span>y=-1/75x+61/3</span></span></span>
