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 = 12x + 4
y = 12x + 4
y = 2x + 7
y = 2x + 7
y = −12x + 2
y = −12x + 2
y = -2x - 1
First, we need to identify the slope of the line that is perpendicular to y = -2x + 5. The slope of this line is -2 (the coefficient of x). For a line to be perpendicular to another line, its slope must be the negative reciprocal of the other line's slope.
The negative reciprocal of -2 is 1/(-1/-2) = 1/2. So, the slope of the line we're looking for is 1/2.
Next, we use the point-slope form of the equation of a line to find the equation of our line:
y - y1 = m(x - x1),
where m is the slope and (x1, y1) is a point on the line.
Plugging in the slope 1/2 and the point (-2, 3):
y - 3 = (1/2)(x - (-2)),
y - 3 = (1/2)(x + 2),
y - 3 = (1/2)x + 1.
Now, we solve for y:
y = (1/2)x + 1 + 3,
y = (1/2)x + 4.
So, the equation of the line is y = (1/2)x + 4.
None of the options provided directly match this equation, so let's check if any of them could be equivalent by manipulating the coefficients.
y = (1/2)x + 4 doesn't match any of the given options exactly, but if we multiply both the slope and the y-intercept by 2 to clear the fraction, we get:
y = x + 8,
which is still not present in the provided options. The provided options don't seem to contain the correct equation of the line, but based on the work we've done, none of the options given are equations of the line perpendicular to y = -2x + 5 passing through the point (-2, 3). There may have been an error in the options provided.