Question

What is the equation of the line that passes through the points (6,6) and (9,8)?

Answer 1

Y1 - y2
---------
x1 - x2

-4 - (-4)
----------
2 - 0


0
-
2

The slope is 0.
The y-intercept is the point where x = 0. The given points already tell us it's -4.

Now we have the formula of y = mx + b or y = 0x - 4 or just y = -4

Shortcut, since both points have a y value of -4 you could have jumped directly to y = -4

Answer 2

Answer:

$y=\frac{2}{3}x+2$

Step-by-step explanation:

The equation for a line is:

y=mx+b

m=slope

b=y-intercept

x,y=(x,y) coordinate pair

Start by finding the slope. The equation for slope is...

$Slope=\frac{y_2-y_1}{x_2-x_1}$

Plug in the given coordinates into the equation

$Slope=\frac{8-6}{9-6}=\frac{2}{3}$

Now, we can use the slope and an x,y coordinate pair to find the y-intercept...

y=mx+b

6=2/3(6)+b

6=12/3+b

6=4+b

Subtract 4 from both sides

b=2

Therefore the equation is...

$y=\frac{2}{3}x+2$