Answer:
To find the equation of the line that passes through the point (3, 4) and is parallel to the line 4x + y + 1 = 0, we can use the fact that two lines are parallel if and only if they have the same slope. Since the line 4x + y + 1 = 0 is already written in slope-intercept form, we can read the slope directly from the coefficient of x, which is 4. Therefore, the slope of the line we are trying to find is also 4.
We can use this slope, along with the point (3, 4), to write the equation of the line in slope-intercept form, which is given by the equation y = mx + b, where m is the slope and b is the y-intercept. To find the y-intercept, we can substitute the values for x and y into the equation and solve for b:
4 = 4(3) + b
Solving for b, we get:
b = -8
Therefore, the equation of the line that passes through the point (3, 4) and is parallel to the line 4x + y + 1 = 0 is:
y = 4x - 8
This is the final answer.
Explanation: