Question

What is an equation of the line that passes through the point left bracket, 2, comma, minus, 1, right bracket(2,−1) and is perpendicular to the line 2, x, minus, y, equals, 42x−y=4?

Answer 1

To find the equation of a line that is perpendicular to a given line and passes through a given point, we can use the point-slope form of the equation. The slope of the given line is 2, so the slope of the perpendicular line is -1/2. By substituting the values of the point and the slope into the point-slope form, we can determine the equation of the perpendicular line as y = -1/2x.

Step-by-step explanation:

To find the equation of a line that is perpendicular to a given line, we need to first find the slope of the given line. The given line has the equation 2x - y = 4. By rearranging the equation into the form y = mx + b, we can see that the slope of the given line is 2.

Since the line we are looking for is perpendicular, its slope will be the negative reciprocal of the given line's slope. So the slope of the line we are looking for is -1/2.

Next, we use the point-slope form of the equation, y - y1 = m(x - x1), where (x1, y1) is the given point (2, -1) and m is the slope. Substituting the values, we get the equation y - (-1) = -1/2(x - 2), which simplifies to y + 1 = -1/2x + 1. Rearranging the equation, we get the final equation of the line as y = -1/2x.