Answer:
3x -y = 2
Explanation:
You want a standard form equation for the line through the points (0, -2) and (2, 4).
Slope
The slope of the line is the "rise" divided by the "run". The given point on the right is 3 grid squares above the one on the left. It is one grid square to the right. So, the slope is ...
m = (squares above)/(squares to the right) = 3/1 = 3
If we consider the actual x- and y-values represented by these grid squares, then the slope is ...
m = (4 -(-2))/(2 -0) = 6/2 = 3
Intercept
The point (0, -2) tells you the y-intercept is -2. That is where the line crosses the y-axis.
Slope-intercept equation
With this information, we can write the slope-intercept form equation for the line:
y = mx +b . . . . . . . line with slope m and y-intercept b
y = 3x -2 . . . . . . . . line with slope 3 and y-intercept -2
Standard form
The standard form of an equation for a line is ...
ax +by = c
where a, b, c are generally mutually-prime integers with a ≥ 0. If a=0, then b > 0.
We can rearrange the slope-intercept equation to put it into this form.
y = 3x -2
3x -y -2 = 0 . . . . . subtract y
3x -y = 2 . . . . . . . add 2. This is the standard-form equation of the line.