What is an equation of the line that passes through the points ( 8 , − 4 ) (8,−4) and ( 6 , − 5 ) (6,−5)? Put your answer in fully reduced form.

Answer 1

Let point A = (6,-5) = (x1,y1) and point B = (8,-4) = (x2,y2). Notice that x2 = 8 > 6 = x1 and y1 = -5 < y2 = -4. Therefore, the slope from point A to point B is positive....

If we draw a line from A to B, we create a right triangle with components

x = distance (6 to 8) = +2 and y = distance (-5 to -4) = +1.

Therefore, change in y = +1 and change in x = +2 --> slope = change in Y divided by change in X = 1/2.

To find y-intercept, take the distance in the X-direction from point A to the origin (x = 0). For this case, we must travel 6 units to the left (x = 6) to (x = 0).

Next, multiple the slope by the negative distance traveled **(positive distance is to the right and negative distance is to the left).

slope = 1/2

negative distance = -6

--> 1/2*-6 = -3.

Now, add -3 to the y coordinate at point A... -3 + -5 = -8 = y-intercept.

Using the form: y = mx + b where m is slope and b = y-intercept, it follows that

y = 1/2x -8

Check:

When x = 6 (point A), y = 1/2*6 -8 = 3 -8 = -5✔

When x = 8 (point B), y = 1/2*8 - 8 = 4 - 8 = -4 ✔