Write an equation for the line that is parallel to the given line and passes through the given point.
y = 3x + 6 ; (2, 4)
To find the equation for the line parallel to y = 3x + 6 and passing through the point (2, 4), we need to use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
Since the line we want is parallel to y = 3x + 6, it will have the same slope. The slope of y = 3x + 6 is 3.
So, our equation will have a slope of 3.
To find the y-intercept, we can plug in the coordinates of the given point (2, 4) into the equation y = mx + b.
4 = 3(2) + b
4 = 6 + b
Now, solve for b:
b = 4 - 6
b = -2
The y-intercept is -2.
So, the equation for the line parallel to y = 3x + 6 and passing through the point (2, 4) is:
y = 3x - 2