Answer:
y = 3x - 9
Step-by-step explanation:
Let's start by finding the slope of the line:
The formula for slope is [tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex].
Plug in the numbers and solve:
[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]
[tex]m = \frac{-3 - (-6)}{2 - 1}[/tex]
[tex]m = \frac{3}{1}[/tex]
[tex]m = 3[/tex]
The slope of the line is 3.
The slope intercept form of a line is y = mx + b, where m is the slope and b is the y coordinate of the y-intercept.
Plugging in the number we got for the slope, the equation becomes:
y = 3x + b
Let's solve for b by plugging in an ordered pair for y and x:
y = 3x + b
-3 = 3(2) + b
-3 = 6 + b
b = -9
The y-coordinate of the line is (0, -9).
Now, plugging in the number into our equation, we get:
y = 3x + (-9)
y = 3x - 9
And that's the equation of the line!
