Question

Find the equation of a line parallel to6, x, plus, y, equals, minus, 66x+y=−6that passes through the point left bracket, 4, comma, 1, right bracket(4,1).

Answer
Multiple Choice Answers
y, equals, one sixth, x, minus, 6y=
6
1
​
x−6
y, equals, minus, 6, x, plus, 25y=−6x+25
y, equals, 6, x, plus, 25y=6x+25
y, equals, minus, one sixth, x, minus, 6y=−
6
1
​
x−6

Answer 1

The equation of the line parallel to 6x + y = -6 that passes through (4,1) is y = -6x + 25. This is found by determining the slope of the given line (-6) and using the point-slope form to find the new line's equation.

Step-by-step explanation:

To find the equation of a line parallel to 6x + y = -6 that passes through the point (4,1), we need to identify the slope of the original line and use it to construct the new line equation. The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept.

The given equation can be rewritten in slope-intercept form to identify the slope:

• 6x + y = -6
• y = -6x - 6

From here, we can see that the slope of the original line is -6. Since parallel lines have the same slope, our new line will also have a slope of -6. Substituting the slope and the coordinates of the given point (4,1) into the slope-intercept equation, we get:

• y - 1 = -6(x - 4)
• y - 1 = -6x + 24
• y = -6x + 25

Therefore, the equation of the line parallel to 6x + y = -6 and passing through the point (4,1) is y = -6x + 25.