Question

Find the equation of a line that passes through (2,12) and is parallel to the graph of y = 3x + 3. Write the equation in slope-intercept form, if possible.

Select the correct choice below and fill in the answer box to complete your choice.
A. The equation of the parallel line in slope-intercept form is
(Simplify your answer.) Type your answer in slope-intercept form. (Use integers or fractions for any numbers in the equation.)
B. The equation of the parallel line cannot be written in slope-intercept form. The equation of the parallel line is: (Simplify your answer.) (Use integers or fractions for any numbers in the equation.)

Answer 1

To find the equation of a line parallel to y = 3x + 3 and passing through (2,12), we need to determine the slope of the given line and use it to construct the equation of the new line.

Step-by-step explanation:

To find the equation of a line parallel to y = 3x + 3 and passing through (2,12) in slope-intercept form, we need to determine the slope of the given line and use it to construct the equation of the new line.

The given line has a slope of 3, which means any line parallel to it will also have a slope of 3. Therefore, the slope of the new line is 3.

Using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, we can substitute the slope and the coordinate (2,12) to find the equation. Since the line passes through (2,12), we have 12 = 3(2) + b. Solving for b, we get b = 6.

Therefore, the equation of the parallel line in slope-intercept form is y = 3x + 6.