Question

What is an equation of the line that passes through the point left bracket, minus, 4, comma, minus, 7, right bracket(−4,−7) and is perpendicular to the line x, plus, 2, y, equals, 4x 2y=4?

Answer 1

The equation of the line that passes through the point (-4,-7) and is perpendicular to the line x + 2y = 4 is y = 2x + 1.

Step-by-step explanation:

To find the equation of a line that is perpendicular to the line x + 2y = 4, we need to determine the slope of the given line and then find the negative reciprocal of this slope. The original line can be rewritten in slope-intercept form as y = (-1/2)x + 2. So, the slope of the given line is -1/2. The negative reciprocal of -1/2 is 2.

Since the line passes through the point (-4,-7), we can use the point-slope form of a linear equation to find the equation of the perpendicular line. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Substituting the values, we get y - (-7) = 2(x - (-4)), which simplifies to y + 7 = 2(x + 4). Expanding and rearranging the equation, we find that the equation of the perpendicular line is y = 2x + 1.

Answer 2

To find the equation of a line perpendicular to a given line, first determine the slope of the given line. Then, use the point-slope form of a linear equation to write the equation of the perpendicular line.

Step-by-step explanation:

To find the equation of a line perpendicular to a given line, we first need to determine the slope of the given line. The given line has the equation x + 2y = 4, which can be rewritten as 2y = -x + 4 or y = -0.5x + 2. The slope of this line is -0.5.

A line perpendicular to this given line will have a slope that is the negative reciprocal of -0.5, which is 2. So, the slope of the perpendicular line is 2.

Now that we have the slope of the perpendicular line and a given point (-4,-7), we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Plugging in the values, we get y - (-7) = 2(x - (-4)), which simplifies to y + 7 = 2(x + 4).

Therefore, the equation of the line that passes through the point (-4,-7) and is perpendicular to the line x + 2y = 4 is y + 7 = 2(x + 4).