Sure, here's how you can solve this problem step by step:
1. Start with the equation of the line given to find the slope. The original line is y = 3x + 2. When a line is in slope-intercept form y=mx+c, the coefficient of x (which is 3 in this case) is the slope. Since two lines are parallel if they have the same slope, the slope (m) of the new line will also be 3.
2. The problem also tells us that this new line passes through the point (-6, 5). This is the x and y coordinates of a point (x1, y1) on the line.
3. We know the form of the line (y = mx + c), the slope of the line (m) and a point on the line (x1, y1). We can use these to find the y-intercept (c) of the line.
4. To do this, we substitute m, x1 and y1 into the line equation and solve for c. Plugging in the known values, we get:
5 = 3*(-6) + c
which simplifies to:
c = 5 - 3*(-6)
which further simplifies to:
c = 23
5. Now that we have the slope and y-intercept of the line, we can plug them into the y = mx + c form to get the equation of the line. The equation of the line is:
y = 3x + 23
This line is parallel to the given line (y = 3x + 2) and passes through the specified point (-6,5).