Question

PLS HELP 30 POINTS!!! What is an equation of the line that passes through the point (-1, -6) and is perpendicular to the line

x+4y= 12?

Answer 1

To find the equation of a line perpendicular to another line, determine the slope of the original line and then find its negative reciprocal. Use the point-slope form of a linear equation to find the equation of the perpendicular line.

Step-by-step explanation:

To find the equation of a line that is perpendicular to another line, we need to determine the slope of the original line and then find its negative reciprocal. The given line x+4y=12 can be rewritten as y = -1/4x + 3. The slope of this line is -1/4, so the slope of the perpendicular line is 4.

Now we can use the point-slope form of a linear equation to find the equation of the perpendicular line. Plug in the coordinates of the given point (-1,-6) and the slope 4 into the equation y - y1 = m(x - x1). In this case, the equation of the perpendicular line is y - (-6) = 4(x - (-1)), which simplifies to y + 6 = 4x + 4.

The equation of the line that passes through the point (-1,-6) and is perpendicular to the line x+4y=12 is y = 4x - 2.

Answer 2

To find the equation of a line that is perpendicular to the given line and passes through the point (-1, -6), we need to find the slope of the given line, which is -1/4. The slope of the line we're looking for will be the negative reciprocal of -1/4, which is 4. Using the point-slope form of a linear equation, we can substitute the point (-1, -6) and the slope 4 to find the equation of the line, which is y = 4x + 2.

Step-by-step explanation:

To find the equation of a line that is perpendicular to another line, we need to find its slope. The given line has the equation x + 4y = 12. To find its slope, we need to rearrange the equation in slope-intercept form, y = mx + b.

Rearranging the given equation, we get 4y = -x + 12, and then dividing both sides by 4, we get y = -1/4x + 3. So, the slope of the given line is -1/4.

Since the line we're looking for is perpendicular to the given line, its slope will be the negative reciprocal of -1/4, which is 4. Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is a point on the line, we can substitute the point (-1, -6) and the slope 4 to find the equation of the line.

Plugging in the values, we get y - (-6) = 4(x - (-1)), which simplifies to y + 6 = 4(x + 1). Expanding and rearranging, we get y = 4x + 2.