1. Find the slope
Slope = (y2 - y1)/(x2 - x1) = (-4 - (-3))/(-1 - 2) = 1/3
Slope = change in y / change in x
Translation: Every time y increases by 1/3, x increases by 1
OR, every time y increases by 1, x increases by 3
Both interpretations follow what we see when graphing the line.
2. Graph the line
3. Find the y-intercept
Definition of y-intercept: the value of y when x = 0
Start at the point (-1,-4), go up by 1/3 and right by 1, since that follows the slope we found and gets us to where x = 0
We know y = -4 when x = -1. If x moves right by 1 unit, then y must move up by 1/3 of a unit
(-4) + (1/3) = (-12/3) + (1/3) = -11/3 = y-intercept
4. Write this information in slope-intercept form:
Slope-Intercept Form: y = mx + b, where m is the slope and b is the y-intercept.
Plug in the values we found for the slope and y-intercept
y = (1/3)x + ((-11)/3) = (1/3)x - (11/3)
5. Convert to Standard Form
Standard Form: Ax + By = C where A, B, and C are constants
Manipulate the Slope-Intercept equation above to find the standard form
Multiply both sides of the slope-intercept form by 3
Subtract x from both sides of the equation
You get 3y - x = -11, which is the answer