Find an equation of the line through (4,6) and parallel to y=3x+4

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 always equivalent 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.