Explanation:
To find the equation of a line that is parallel to the given line y = 9 + 3x and passes through the point (-3, 5), you can use the fact that parallel lines have the same slope.
The slope of the given line y = 9 + 3x is 3 (the coefficient of x).
So, the equation of the new line with the same slope that passes through (-3, 5) can be written as:
y = mx + b
where m is the slope (which is 3), and b is the y-intercept that we need to find.
Now, substitute the coordinates of the given point (-3, 5) into the equation:
5 = 3*(-3) + b
Now, solve for b:
5 = -9 + b
Add 9 to both sides:
b = 5 + 9
b = 14
So, the equation of the new line that is parallel to y = 9 + 3x and passes through (-3, 5) is:
y = 3x + 14