find slope of line through (2,0) and (5,6)

Question

find the slope of the line through the pair of points (2,0) and (5,6), then name another point on the same line

Answer 1

Alaysiah:

Since you have 2 points, just use the simple slope formula. SLOPE, or m = (y2-y1)/(x2-x1). Note that x2 means x sub 2 ....not x squared. The number is a subscript or a counter, not an exponent.

It doesn't matter which point you call Point 1 or point 2. For the sake of simplicity we will call the point (2,0) point 1 so x1=2 and y1 = 0. Therefore point 2 is (5,6) so x2 = 5 and y2 = 6. Now we substitute:

(6 - 0)/ ( 5 - 2) = 6/3 = 2. So the slope is 2.

Another way to find a second point is to get the equation of the line containing those 2 points.

y = mx + b is the general equation of a straight line. We know the slope, m is 2. To get the y intercept, b, plug in x and y using the point ( 2,0). We could have used the other point, but 0 is very easy to work with.

So we have y = mx + b or....0 = 2( 2 is m) X (2, this second 2 is the x component) + b...

0 = 2(2) + b. or...0 = 4 + b. Clearly b = -4. So the final equation is y = 2x-4. Now you can plug in any input value ( x value) and get a corresponding output (y value). Let's plug in x = 9. We have y = 2(9) - 4...y = 14. So another point is ( 9,14).

Let's plug in another x value. Let's try 6. So.. y = 2(6) - 4. Clearly y = 12-4 = 8. So another point is ( 6,8)

So...2 other points are (9,14) and ( 6,8). Knowing the equation of the line you can easily find as many points as you want.

Answer 2

slope between two point (x1,y1) and (x2,y2) is (y2-y1)/(x2-x1)

here (x1,y1) is (2,0) and (x2,y2) is (5,6) so slope is (6-0)/(5-2) = 2

slope is change in y/change in x. so for every change in y of 2, x changes 1.

so can use that to find next point after (5,6)

change x 1 and change y 2 and you get (6,8).