Write an equation of a line in slope intercept form that is parallel to y = 3x+6 and passes through the point (-10, 2.5). Do not use spaces and enter fractions as improper reduced fractions when needed.

you know the slope=3, so just plug in your numbers:

2.5 = 3(-10) + c
c = 32.5

y = 3x + 32.5

To find the equation of a line that is parallel to a given line and passes through a specific point, you can follow these steps:

Step 1: Determine the slope of the given line.
The given line has a slope of 3, which is the coefficient of the x-term in the equation y = 3x + 6.

Step 2: Since the parallel line will have the same slope, the equation in slope-intercept form will have the form y = 3x + b, where b is the y-intercept.

Step 3: Use the coordinates of the point (-10, 2.5) to find the value of b and complete the equation.
Substitute the x-coordinate and y-coordinate of the given point into the equation y = 3x + b:
2.5 = 3(-10) + b

Simplify the equation:
2.5 = -30 + b

Step 4: Solve for b.
To isolate b, add 30 to both sides of the equation:
b = 2.5 + 30
b = 32.5

Step 5: Write the final equation.
Now that you have the value of b, you can substitute it back into the equation y = 3x + b:
y = 3x + 32.5

Therefore, the equation of the line in slope-intercept form that is parallel to y = 3x + 6 and passes through the point (-10, 2.5) is y = 3x + 32.5.