Question

The points (6, 9) and (0, 6) fall on a particular line. What is its equation in slope-intercept form?

Answer 1

Answer:

$y = \frac{1}{2}x + 6$

Step-by-step explanation:

$Let \ (x _1 y _ 1 ) = ( 6 , 9 ) \ and \ (x _ 2 , y _ 2 ) \ = ( 0 , 6 )$

Step 1 : Find slope, m

              $slope, m = \frac{y _ 2 - y _ 1}{x_ 2 - x_ 1 } = \frac{6 - 9}{0 - 6 } = \frac{-3}{-6} = \frac{1}{2}$

Step 2 : Find the equation

                $(y - y _ 1 ) = m ( x - x_ 1) \\\\( y - 9 ) = \frac{1}{2} (x - 6 ) \\\\y = \frac{1}{2}x - 3 + 9 \\\\y = \frac{1}{2}x + 6$

Answer 2

Answer:

y = 1/2x + 6

Step-by-step explanation:

y = mx + b is the formula. m is the slope and to calculate that you use the slope formula y2 - y1/ x2 - x1.

(6, 9)  is the first coordinate so 6 is x1 and 9 is y1. Similarly in (0, 6), x2 is 0 and y2 is 6. Now if we put that into the slope formula it would look something like this: 6-9/0-6. that comes to -3/-6. simplify and cancel out the negatives and you get 1/2 which is the m ( slope).

The b is the y-intercept, which is the y value for where the x is 0. In this question, they already give you the coordinate where x is 0. (0, 6). x is 0 and y is 6. therefore the b (y-intercept) is 6.

Put all of this into y =mx +b, and you get y= 1/2x + 6.

If you want to make sure you did it right, just plug in one of the coordinates into this equation. Let's use  (6, 9).

9 = 1/2 (6) + 6

9 = 3 + 6

9 = 9. It works out, therefore the equation right.

Hope this helps