Hello!
To find the equation of line that passes through (4, 6) and is parallel to y = 3x + 4, we need to use the slope of the given line, and also to find the y-intercept. We use the same slope of the old equation to make the new equation because if two lines are parallel, then their slopes are <u>always equivalent</u> to one another.
To find the equation, we need to use slope-intercept form, which is written as y = mx + b, where m is the slope and b is the y-intercept.
y = 3x + b (substitute the given ordered pair into the equation)
6 = 3(4) + b (simplify - multiply)
6 = 12 + b (subtract 12 from btoh sides)
-6 = b
Therefore, the equation of the line that passes through (4, 6) and is also parallel to y = 3x + 4, is y = 3x - 6.
