Question

What is the equation of the line that is perpendicular to y = 2x + 3 and passes through the point (−4, 8)?

y = 2x + 16
y = 2x − 20
y equals negative one-half times x
y equals negative one-half times x plus 6

Answer 1

To find the equation of a line that is perpendicular to a given line and passes through a given point, we can first find the slope of the given line and then use the slope of the perpendicular line, which is the negative reciprocal of the slope of the given line.

The given line is y = 2x + 3, and the given point is (-4, 8). The slope of the given line is 2, so the slope of the perpendicular line is -1/2. This means that the equation of the perpendicular line can be written in the form y = -1/2 * x + b, where b is the y-intercept of the line.

To find the value of b, we can plug the coordinates of the given point into the equation of the line and solve for b. So, if we plug in x = -4 and y = 8 into the equation y = -1/2 * x + b, we get the following:

8 = -1/2 * (-4) + b

8 = 2 + b

6 = b

Therefore, the equation of the line that is perpendicular to y = 2x + 3 and passes through the point (-4, 8) is y = -1/2 * x + 6. This means that the correct answer is y = -1/2 * x + 6.

Answer 2

The slope of a line perpendicular to y = 2x + 3 is the negative reciprocal of the slope of y = 2x + 3, which is -1/2. Therefore, the equation of the line that is perpendicular to y = 2x + 3 and passes through the point (-4,8) has the form y = -1/2x + b, where b is the y-intercept.

To find the value of b, we can plug in the coordinates of the point (-4,8) into the equation y = -1/2x + b and solve for b:

8 = -1/2(-4) + b

8 = 2 + b

b = 6

Therefore, the equation of the line that is perpendicular to y = 2x + 3 and passes through the point (-4,8) is y = -1/2x + 6. This can also be written as y = -1/2x + 6.