You want to find the equation for a line that passes through the two points:(4,5) and (-6,3).First of all, remember what the equation of a line is:y = mx+bWhere:m is the slope, andb is the y-interceptFirst, let's find what m is, the slope of the line...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, (4,5), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=4 and y1=5.Also, let's call the second point you gave, (-6,3), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-6 and y2=3.Now, just plug the numbers into the formula for m above, like this:m=3 - 5-6 - 4or...m=-2-10or...m=1/5So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:y=1/5x+bNow, what about b, the y-intercept?To find b, think about what your (x,y) points mean:(4,5). When x of the line is 4, y of the line must be 5.(-6,3). When x of the line is -6, y of the line must be 3.Because you said the line passes through each one of these two points, right?Now, look at our line's equation so far: y=1/5x+b. b is what we want, the 1/5 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 (4,5) and (-6,3).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:(4,5). y=mx+b or 5=1/5 × 4+b, or solving for b: b=5-(1/5)(4). b=21/5.(-6,3). y=mx+b or 3=1/5 × -6+b, or solving for b: b=3-(1/5)(-6). b=21/5.See! In both cases we got the same value for b. And this completes our problem.The equation of the line that passes through the points(4,5) and (-6,3)isy=1/5x+21/5
Y-y1/x-x1 =y2-y1/x2-x1 Y-5/x-4 =3-(5)/3-4 (Y-5)(3-4)=X-4(3-5) Distribute and form the like this ax+by+C=0