Question

Write the equation of a line that passes through the point (4, 0) and is parallel to the line 3x−y=6.

a) 3x−y=−12
b) 3x−y=123
c) x+y=123
d) x+y=−12

Answer 1

The equation of a line parallel to 3x - y = 6 and passing through the point (4,0) is 3x - y = 12. This is found by using the same slope as the given line and applying the point-slope form with the given point.

Step-by-step explanation:

The student is asking for the equation of a line that is parallel to the line given by the equation 3x - y = 6 and passes through the point (4, 0). Two lines are parallel if they have the same slope. The given line can be written in slope-intercept form as y = 3x - 6, which reveals that the slope (m) is 3. To find the equation of a line parallel to the given line and passing through (4, 0), we use the slope 3 and the point (4, 0) in the point-slope form y - y1 = m(x - x1), which gives us:

y - 0 = 3(x - 4)

y = 3x - 12

To find the matching answer choice, we need to rewrite this in the same form as the other equations, resulting in:

3x - y = 12

Therefore, the correct answer from the provided options is b) 3x - y = 12.