you know the slope=3, so just plug in your numbers:
2.5 = 3(-10) + c
c = 32.5
y = 3x + 32.5
2.5 = 3(-10) + c
c = 32.5
y = 3x + 32.5
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.