Write an equation of a line in point-slope form for a line parallel to y = 6x + 2 that contains P ( 5,9).
To find the equation of a line parallel to another line, we need two pieces of information: the slope of the given line and a point that the new line contains.
In this case, the given line is y = 6x + 2. This equation is already in slope-intercept form (y = mx + b), where the coefficient of x (6) represents the slope of the line.
Since we want a line parallel to this given line, the new line will also have a slope of 6.
Now we have the slope (m = 6) and a point P(5,9) that the new line contains. To find the equation of the line, we can use the point-slope form of a line: y - y1 = m(x - x1), where (x1, y1) is the given point.
Substituting the values, we use:
y - 9 = 6(x - 5)
Simplifying:
y - 9 = 6x - 30
Now, we can rewrite the equation in slope-intercept form (y = mx + b) by isolating y:
y = 6x - 21
Therefore, the equation of the line parallel to y = 6x + 2 that contains the point P(5,9) is y = 6x - 21.