There several forms of the equation of a line. Most of us learn the three most common forms, which are (in order from most common to least common):
1. The slope intercept form: y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line meets the y-axis)
2. The point-slope form: y - y1 = m (x - x1), where m is the slope of the line and (x1, y1) are the coordinates of a point on this line.
3. The Standard Form: Ax + By = C, where A, B, and C are real numbers, and A and B are not both zero (A & B cannot be zero simultaneously).
So, now that we know the three forms, we try to figure out which one of the three is easiest to find (unless the question asks to find a specific form), given the information.
Here, we are given the point (4, 12) and the value of the y-intercept -2. This means we are given two points, (4, 12) and (0, -2).
Using this information, we can first find the slope, using the formula: m = (y2 - y1)/(x2 - x1).
Here, m = (12 -(-2))/(4-0) = 14/4 = 7/2
Now that we have the slope and the y-intercept, we can find the equation of this line in slope-intercept form:
y = (7/2)x - 2
I hope this helps,