Answer:
To find the equation of a line that is perpendicular to another line, we need to determine the slope of the given line and then find the negative reciprocal of that slope. The negative reciprocal of a slope is a value obtained by flipping the fraction and changing its sign.
First, let's rearrange the equation 4x - 2y = 7 into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
Starting with 4x - 2y = 7:
-2y = -4x + 7
Dividing both sides by -2:
y = 2x - 7/2
From this equation, we can see that the slope of the given line is 2. To find the negative reciprocal of this slope, we flip the fraction and change its sign. Therefore, the negative reciprocal of 2 is -1/2.
Now that we have determined the slope (-1/2) of the line perpendicular to the given line, we can use it along with the coordinates of the point (-3, 1) to find the equation of the desired line using point-slope form (y - y1 = m(x - x1)).
Substituting x1 = -3, y1 = 1, and m = -1/2 into the point-slope form equation, we get:
y - 1 = (-1/2)(x - (-3))
y - 1 = (-1/2)(x + 3)
y - 1 = (-1/2)x - (3/2)
Simplifying further:
y = (-1/2)x - (3/2) + 1
y = (-1/2)x - (3/2) + (2/2)
y = (-1/2)x - (1/2)
Therefore, the equation of the line that passes through the point (-3, 1) and is perpendicular to the line 4x - 2y = 7 is y = (-1/2)x - (1/2).
Explanation: