Question

What is the equation of the line that is parallel to the line y − 1 = 4(x 3) and passes through the point (4, 32)?

A. y = –x + 33
B. y = –x + 36
C. y = 4x − 16
D. y = 4x + 16

Answer 1

To find the equation of a line that is parallel to the given line and passes through a given point, we need to find the slope of the given line and use it to write the equation in slope-intercept form.

Step-by-step explanation:

To find the equation of a line that is parallel to the line y - 1 = 4(x - 3) and passes through the point (4, 32), we need to find the slope of the given line and then use that slope to write the equation in slope-intercept form.

1. The given line is in the form y - y1 = m(x - x1), where m is the slope of the line. Comparing this with the equation y - 1 = 4(x -3), we can see that the slope is 4.
2. Since the line we are looking for is parallel to the given line, it will also have a slope of 4.
3. Using the point-slope form, we can write the equation of the line as y - y1 = m(x - x1). Substituting the values m = 4, x1 = 4, and y1 = 32 into the equation, we get y - 32 = 4(x - 4).
4. Simplifying the equation, we have y - 32 = 4x - 16.
5. Finally, rearranging the equation in slope-intercept form, we get the equation of the line as y = 4x + 16.