Question

Which of the following is an equation of a line that is perpendicular to y = -2x + 5 and passes through the point (-2, 3)?

Responses

y = -2x - 1

y = 2x + 7

y= - 1/2x +2

y= 1/2x+4

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find a line that is perpendicular to y = -2x + 5, we need to find the negative reciprocal of the slope of this line. The slope of y = -2x + 5 is -2. The negative reciprocal of -2 is 1/2.

Now that we have the slope for the perpendicular line, we can use the point-slope form of a linear equation to find the equation of the line that passes through the point (-2, 3).

The point-slope form is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

Using (-2, 3) as the point and 1/2 as the slope, we can plug in the values and simplify to find the equation of the line:

y - 3 = 1/2(x - (-2))
y - 3 = 1/2(x + 2)
y - 3 = 1/2x + 1
y = 1/2x + 4

Therefore, the equation of the line that is perpendicular to y = -2x + 5 and passes through the point (-2, 3) is y = 1/2x + 4.